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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Publikationen

On a equality for 3-dimensional manifolds.
Thomas Friedrich
Annales Societatis Mathematicae Polonae, Seir X: Commentationes Mathematicae XVIII (1975), 31-32.

 

Über die n-totale Absolutkrümmung der Ordnung beta > 1.
Thomas Friedrich
Colloquium Mathematicum, vol. XXXI Fasc. (1974), 83-86.

 

Berandete Mannigfaltigkeiten in Euklidischen Räumen.
Thomas Friedrich
Demonstratio Mathematica, vol. VII No. 3 (1974), 327-336.

 

A characterization of the disc.
Thomas Friedrich
Colloquium Mathematicum, vol. XXXII, Fasc. 2 (1974), 77-81.

 

Über p-reguläre Abbildungen von Sphären in Grassmannsche Mannigfaltigkeiten.
Thomas Friedrich and Peter Wintgen
Mathematische Nachrichten 66 (1975), 247-253.

 

m-Funktionen and ihre Anwendung auf die totale Absolutkrümmung.
Thomas Friedrich
Mathematische Nachrichten 67 (1975), 281-301.

 

Über SL-Mannigfaltigkeiten.
Thomas Friedrich and Andreas Nestke
Mathematische Nachrichten 85 (1978), 31-36.

 

Eine Bemerkung über das Produkt im Kohomologiering von pi-Mannigfaltigkeiten.
Thomas Friedrich
Mathematische Nachrichten 84 (1978), 329-332.

 

Ein Kriterium für die formale Selbstadjungiertheit des Dirac-Operators.
Thomas Friedrich and Sonja Sulanke
Coll. Math. vol. XL, Fasc. 2 (1979), 239-247.

 

Immersionen höherer Ordnung kompakter Mannigfaltigkeiten in Euklidischen Räumen.
Helga Dlubek and Thomas Friedrich
Beiträge zur Algebra and Geometrie, Heft 9 (1980), 83-101.

 

Vorlesungen über K-Theorie.
Thomas Friedrich
Teubner-Verlag Leipzig 1978.

 

Spectral properties of the Dirac operator
Helga Dlubek and Thomas Friedrich
Bulletin de L'Academie Polonaise de Sciences, Series des Sciences Mathematiques
vol. XXVII No. 7-8 (1979), 621-624.

 

Spektraleigenschaften des Dirac-Operators - die Fundamentallösung seiner Wärmeleitungsgleichung
and die Asymptotenentwicklung der Zeta-Funktion

Helga Dlubek and Thomas Friedrich
Journal of Differential Geometry 15 (1980), 1-26.

 

Zur Existenz paralleler Spinorfelder über Riemannschen Mannigfaltigkeiten.
Thomas Friedrich
Czechoslavakian-GDR-Polish scientific school on differential geometry
Boszkowo/ Poland 1978, Sci. Comm., Part 1,2; 104-124 (1979)

 

Zur Existenz paralleler Spinorfelder über Riemannschen Mannigfaltigkeiten.
Thomas Friedrich
Colloquium Mathematicum vol. XLIV, Fasc. 2 (1981), 277-290.

 

Die Abhängigkeit des Dirac-Operators von der Spin-Struktur.
Thomas Friedrich
Czechoslavakian-GDR-Polish scientific school on differential geometry
Boszkowo/ Poland 1978, Sci. Comm., Part 1,2; 74-103 (1979)

 

Die Abhängigkeit des Dirac-Operators von der Spin-Struktur.
Thomas Friedrich
Colloquium Mathematicum vol. XLVII, Fasc. 1 (1984), 57-62.

 

Der erste Eigenwert des Dirac-Operators einer kompakten Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
Thomas Friedrich
Mathematische Nachrichten 97 (1980), 117-146.

 

Self-duality of Riemannian manifolds and connections.
Thomas Friedrich
in: Riemannian Geometry and Instantons, Teubner-Verlag Stuttgart, 56-104.

 

Compact four-dimensional self-dual Einstein manifolds with positive scalar curvature.
Thomas Friedrich and Herbert Kurke
Mathematische Nachrichten 106 (1982), 271-299.

 

A geometric introduction to Yang-Mills-Equations
Thomas Friedrich
Proceedings of the 5. Scheveningen Conference on Differential Equations.
Lecture Notes in Mathematics No. 926 (1982), 74-84.

 

Probleme der Globalen Analysis mit Anwendungen auf homogene Räume.
Thomas Friedrich
Mitteilungen der Mathematischen Gesellschaft der DDR Heft 2/4 (1981), 167-183.

 

Note on fibrations of U(2) over S^2
Thomas Friedrich
Mathematische Nachrichten 120 (1985), 139-140.

 

On surfaces in four-spaces.
Thomas Friedrich
Annals of Global Analysis and Geometry vol. 2 No. 3 (1984), 257-287.

 

A remark on the first eigenvalue of the Dirac operator on 4-dimensional manifolds.
Thomas Friedrich
Mathematische Nachrichten 102 (1981), 53-56.

 

Obituary. Peter Wintgen (1945-1981)
H.G. Bothe, Th. Friedrich and R. Sulanke
Annals of Global Analysis and Geometry 2 (1984), 88-89.

 

In memorian Peter Wintgen (2.11.1945 - 17.7.1981)
H.G. Bothe, Th. Friedrich and R. Sulanke
Mitteilungen der Mathematischen Gesellschaft der DDR No. 4 (1984), 25-26.

 

On Einstein metrics on the twistor space of a four-dimensional Riemannian manifold
Thomas Friedrich and Ralf Grunewald
Mathematische Nachrichten 123 (1985), 55-60.

 

An application of the twistor theory to surfaces in 4-dimensional manifolds.
Thomas Friedrich
Proceedings of the Conference on Differential Geometry and its Applications, Nove Mesto 1983, 42-45.

 

Yang-Mills Equations on the two-dimensional sphere.
Thomas Friedrich and Lutz Habermann
Communications in Mathematical Physics 100 (1985), 231-243.

 

A group-theoretical study of the stabilizer of a generic connection.
Helga Baum and Thomas Friedrich
Annals of Global Analysis and Geometry vol. 3 No. 1 (1985), 120-128.

 

On the first eigenvalue of the Dirac operator on 6-dimensional manifolds.
Thomas Friedrich and Ralf Grunewald
Annals of Global Analysis and Geometry vol. 3 No. 3 (1985), 265-273.

 

The geometry of t-holomorphic surfaces in S^4.
Thomas Friedirch
Mathematische Nachrichten 137 (1988), 49-62.

 

Einstein manifolds of dimension five with small first eigenvalue of the Dirac operator.
Thomas Friedrich and Ines Kath
Journal of Differential Geometry vol. 29 No. 2 (1989), 263-279.

 

Riemannian manifolds with small eigenvalues of the Dirac operator.
Thomas Friedrich
Proceedings of the 27th Arbeitstagung, Bonn 12. - 19.06.1987, Preprint MPI.

 

Compact 5-dimensional Riemannian manifolds with parallel spinors
Thomas Friedrich and Ines Kath
Mathematische Nachrichten 147 (1990), 161-165.

 

Varietes riemanniennes compactes de dimension 7 admettant des spineurs de Killing.
Thomas Friedrich and Ines Kath
C.R. Acad. Sci. Paris t. 307, Serie 1 (1988), 967-969.

 

7-dimensional compact Riemannian manifolds with Killing spinors.
Thomas Friedrich and Ines Kath
Communication in Mathematical Physics 133 (1990), 543-561.

 

On the conformal relation between twistors and Killing spinors.
Thomas Friedrich
Supplemento de Rendiconti des Circole Mathematico de Palermo, Serie II, No. 22 (1989), 59-75.

 

Die Fisher-Information und symplektische Strukturen.
Thomas Friedrich
Mathematische Nachrichten 153 (1991), 273-296.

 

Twistor spinors and the solutions of the equation (E) on Riemannian manifolds.
Thomas Friedrich and Olga Pokorna
Supplemento de Rendiconti des Circole Mathematico de Palermo, Serie II, No. 26 (1991), 149-153.

 

Twistors and Killing Spinors on Riemannian Manifolds.
Helga Baum, Thomas Friedrich, Ralf Grunewald and Ines Kath
Teubner-Verlag Leipzig / Stuttgart

 

The classification of 4-dimensional Kähler manifolds with small eigenvalue of the Dirac operator.
Thomas Friedrich
Mathematische Annalen 295 (1993), 565-574.

 

Eigenvalues of the Dirac operator, Twistors and Killing spinors on Riemannian manifolds.
Helga Baum and Thomas Friedrich
In: "Clifford Algebras and Spinor Structures", (ed. by R. Ablamowicz and R. Lounesto)
Kluwer Academic Publisher 1995, 243-256.

 

Harmonic spinors on conformally flat manifolds with S^1-symmetry.
Thomas Friedrich
Mathematische Nachrichten 174 (1995), 151-158.

 

Neue Invarianten der 4-dimensionalen Mannigfaltigkeiten.
Thomas Friedrich
Preprint SFB 288 No. 156 (1995).

 

Seiberg-Witten theory.
Jürgen Eichhorn and Thomas Friedrich
Banach Center Publications vol. 39, Polish Academy of Sciences Warsaw 1997, 231-267.

 

On nearly parallel G2-structures
Thomas Friedrich, Ines Kath, Uwe Semmelmann and Andrei Moroianu
Journal of Geometry and Physics 23 (1997), 259-286. [ps-file]

 

On Superminimal Surfaces
Thomas Friedrich
Archivum Mathematicum vol. 33 (1997), 41-56. [ps-file]

 

Dirac-Operatoren in der Riemannschen Geometrie
Thomas Friedrich
Braunschweig, Wiesbaden: Vieweg 1997.

 

Clifford Structures and Spinor Bundles
Thomas Friedrich and Andrzej Trautman
SFB 288 Preprint Nr. 251, 1997, [ps-file]

 

On the Spinor Representation of Surfaces in Euclidean 3-Spaces
Thomas Friedrich
Journal of Geometry and Physics 28 (1998) 143-157, [ps-file]

 

The Gaussian Measure on Algebraic Varieties
Ilka Agricola and Thomas Friedrich
Fundamenta Mathematica 159 (1999), 91-98, [ps-file]

 

Upper bounds for the first eigenvalue of the Dirac operator on surfaces
Ilka Agricola and Thomas Friedrich
Journ. Geom. Phys. 30 (1999), 1-22, [ps-file]

 

A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus
Ilka Agricola, Bernd Ammann, Thomas Friedrich
Manuscripta Math. 100 (1999) , 231 - 258, [ps-file]

 

The Einstein-Dirac Equation on Riemannian Spin Manifolds
Th. Friedrich and Eui Chul Kim
Journ. Geom. Phys. 33 (2000), 128-172, [ps-file]

 

A geometric estimate for a periodic Schrödinger operator whose potential is the curvature of a spherical curve
Th. Friedrich
Coll. Mathematicum Vol. 83 (2000) No. 2, 209-216, [ps-file]

 

Spin spaces, Lipschitz groups and spinor bundles
Th. Friedrich and A. Trautman
Ann. Glob. Anal. Geom. 18 No. 3-4 (2000), 221-240, [pdf-file].

 

Solutions of the Einstein-Dirac Equation on Riemannian 3-Manifolds with Constant Scalar Curvature.
Th. Friedrich
Journ. Geom. Phys. 36 (2000), 199-210, [ps-file]

 

New Solutions of the Einstein-Dirac Equation in Dimension n=3.
Th. Friedrich
math.DG/0001156, SFB 288 Preprint No. 443 (2000), [ps-file]

 

Dirac Operators in Riemannian Geometry.
Thomas Friedrich
Graduate Studies in Mathematics 25, AMS, Providence, Rhode Island, 2000.

 

Some Remarks on the Hijazi Inequality and Generalizations of the Killing Equation for Spinors.
Th. Friedrich and Eui-Chul Kim
Journ. Geom. Phys. 37 (2001), 1-14, [ps-file]

 

Globale Analysis - Differentialformen in Analysis, Geometrie und Physik.
I. Agricola und Th. Friedrich
Vieweg Verlag 2001, [Präsentation]

 

Weak Spin(9)-Structures on 16-dimensional Riemannian Manifolds.
Th. Friedrich
Asian Journal of Mathematics 5 (2001), pp. 129-160. [ps-file]

 

Cartan Spinor Bundles on Manifolds
Th. Friedrich
Proc. XVII Workshop on Geometric Methods in Physics, Bialowieza, July 3-9, 1998, Wydawnictwa Uniwersytetu Warszawskiego 2001, pp. 253-261, [ps-file]

 

Eigenvalue estimates for the Dirac operator depending on the Weyl tensor.
Th. Friedrich (Berlin) and Klaus-Dieter Kirchberg (Berlin)
Journ. Geom. Phys. 41 (2002), 196-207, [ps-file],

 

Parallel spinors and connections with skew-symmetric torsion in string theory.
Th. Friedrich (Berlin) and St. Ivanov (Sofia)
Asian Journ. Math. 6 (2002), 303-336, [ps-file],

 

Eigenvalue estimates of the Dirac operator depending on the Ricci tensor.
Th. Friedrich (Berlin) and Klaus-Dieter Kirchberg (Berlin)
Math. Ann. 324, 799-816 (2002), [ps-file],

 

Global Analysis: Differential Forms in Analysis, Geometry and Physics.
I. Agricola and Th. Friedrich (Berlin)
AMS Publications 2002, GMS 52
[AMS link] [errata]

 

On types of non-integrable geometries.
Th. Friedrich (Berlin)
Rend. del Circ. Mat. di Palermo 72 (2003), 99-113, [ps-file],

 

Spin(9)-structures and connections with totally skew-symmetric torsion.
Th. Friedrich (Berlin)
Journ. Geom. Phys. 47 (2003), 197-206, [ps-file],

 

Almost contact manifolds, connections with torsion and parallel spinors.
Th. Friedrich (Berlin) and Stefan Ivanov (Sofia)
J. Reine Ang. Math. 559 (2003), 217-236, [ps-file],

 

Killing spinor equations in dimension 7 and geometry of integrable G_2-manifolds.
Th. Friedrich (Berlin) and Stefan Ivanov (Sofia)
math.DG/0112201, Journ. Geom. Phys. 48 (2003), 1-11, [ps-file],

 

Killing spinors in supergravity with 4-fluxes.
I. Agricola and Th. Friedrich (Berlin)
math-DG/0307360, Class. Quantum Grav. 20 (2003), 4707-4715, [ps-file]

 

The Casimir operator of a metric connection with skew-symmetric torsion.
I. Agricola and Th. Friedrich (Berlin)
math-DG/0305233, Journ. Geom. Phys. 50 (2004), 188-204, ps-file

 

On the holonomy of connections with skew-symmetric torsion.
I. Agricola and Th. Friedrich (Berlin)
math-DG/0305069, Math. Ann. 328 (2004), 711-748, [ps-file]

 

Almost Hermitian 6-Manifolds Revisited.
Bogdan Alexandrov, Thomas Friedrich and Nils Schoemann (Berlin)
math-DG/0403131, Journ. Geom. Phys. 53 (2005), 1--30,
ps-file

 

On the Ricci tensor in the common sector of type II string theory.
Ilka Agricola, Thomas Friedrich, Paul-Andy Nagy, Christof Puhle (Berlin)
hep-th/0412127, Class. Quantum Grav. 22 (2005), 2569-2577
ps-file

 

Elementargeometrie - Fachwissen für Studium und Mathematikunterricht.
Ilka Agricola, Thomas Friedrich (Berlin)
Vieweg-Verlag, April 2005
Präsentation

 

Geometric structures of vectorial type.
Ilka Agricola and Thomas Friedrich (Berlin)
Journ. Geom. Physics 56 (2006), pp. 2403-2414, math.DG/0509147. [pdf-file],

 

Nearly Kähler and nearly parallel G_2-structures on spheres.
Th. Friedrich (Berlin)
Archivum Mathematicum, Tomus 42 (2006), Supplement, 241-243, math.DG/0509146 [ps-file],

 

G_2-manifolds with parallel characteristic torsion.
Th. Friedrich (Berlin)
Journ. Differential Geometry and its Applications 25 (2007), 632-648, math.DG/0604441 (2006) [ps-file],

 

Elementary Geometry.
I. Agricola and Th. Friedrich (Berlin)
Publications of the AMS, Student Mathematical Library Vol. 43 (2008),

 

Eigenvalues estimates for the Dirac operator in terms of Codazzi tensors.
Th. Friedrich, E.C. Kim
Bull. Korean Math. Soc. 45, No. 2 (2008), pp. 365-373, arXiv: 0709.0780v1 [math.DG] (2007) [pdf-file], [link]

 

Eigenvalue estimates for Dirac operators with parallel characteristic torsion.
I. Agricola, Th. Friedrich, and M. Kassuba (Berlin)
Diff. Geom. and its Appl. 26 (2008), 613-624, math.DG/0612304 (2006) [pdf-file],

 

Elementargeometrie - Fachwissen für Studium und Mathematikunterricht.
Ilka Agricola, Thomas Friedrich (Berlin)
Vieweg-Verlag, 2008 (zweite Auflage)

 

3-Sasakian manifolds in dimension seven, their spinors and G_2 structures.
Ilka Agricola, Thomas Friedrich (Berlin)
Journ. Geom. Phys. 60 (2010), 326-332, arXiv.org - 0812.1651, [pdf-file]

 

Vektoranalysis - Differentialformen in Analysis, Geometrie und Physik.
Ilka Agricola (Marburg), Thomas Friedrich (Berlin)
Vieweg + Teubner, März 2010 (zweite Auflage)

 

A note on flat metric connections with antisymmetric torsion.
Ilka Agricola, Thomas Friedrich (Berlin)
Diff. Geom. its Appl. 28 (2010), 480-487, arXiv.org - 0911.1602, [pdf-file]

 

On the topology and the geometry of SO(3)-manifolds.
Ilka Agricola (Marburg), Julia Becker-Bender (Marburg), Thomas Friedrich (Berlin)
Ann. Glob. Anal. Geom. 40, No. 1 (2011), 67-84, [Springer-Link], arXiv.org - 1010.0260

 

The second Dirac eigenvalue of a nearly parallel G_2-manifold.
Thomas Friedrich (Berlin)
Advances in Applied Clifford Algebras 22, No. 2 (2012), pp. 301-311, [Springer-Link], arXiv.org - 1104.0745

 

Sp(3) structures on 14-dimensional manifolds.
Ilka Agricola (Marburg), Thomas Friedrich (Berlin), Jos Höll (Marburg)
Journ. Geom. Phys. (69) 2013, pp. 12-30. DOI information: 10.1016/j.geomphys.2013.02.010, arXiv.org - 1210.3056, [pdf-file]

 

Cocalibrated G_2-manifolds with Ricci flat characteristic connection.
Thomas Friedrich (Berlin)
Comm. in Mathematics, Vol. 21 (2013), 1-13; arXiv.org - 1303.7444, [pdf-file]

 

The classification of naturally reductive homogeneous spaces in dimensions n \le 6.
Ilka Agricola (Marburg), Ana Cristina Ferreira (Braga/Marburg), Thomas Friedrich (Berlin)
Diff. Geom. its Appl. Vol. 39 (2015), 59-92, arXiv.org:1407.4936, [pdf-file]
 
Spinorial description of SU(3)- and G_2-manifolds.
Ilka Agricola (Marburg), Simon G. Chiossi (Salvador, Brazil), Thomas Friedrich (Berlin), and Jos Höll (Marburg)
Journ. Geom. Phys. Vol. 98 (2015), 535-555; arXiv.org:1411.5663, [pdf-file]
 
S⁶ and the geometry of nearly Kähler 6-manifolds.
Ilka Agricola (Marburg), Aleksandra Borowka (Krakow), Thomas Friedrich (Berlin)
      Diff.Geom. its Appl. 57 (2018), 75-86, arXiv.org:1707.08591, [pdf-file]
 
 
Buchbesprechung.
Thomas Friedrich (Berlin)
erscheint in Jahresbericht Deutsche Mathematiker-Vereinigung vol. 118, Issue 1 (March 2016), 51-56. [pdf-file]