Selected publications by our research group (differential geometry and topology)

Textbooks:

• W. Kühnel, Matrizen und Lie-Gruppen, eine geometrische Einführung, Vieweg+Teubner 2011
• W. Kühnel, Differentialgeometrie, Kurven - Flächen - Mannigfaltigkeiten, Vieweg 1999,
  2. Auflage 2003, 3. Auflage 2005, 4. Auflage 2008, 5. Auflage Vieweg+Teubner 2010, 6. Auflage Springer Spektrum 2013
  English version: Differential Geometry, Curves - Surfaces - Manifolds, translated from the German by B.Hunt,
  AMS Student Mathematical Library Series Vol. 16, American Mathematical Society 2002, 2nd edition 2006

Survey Articles, Monographs:

• W. Kühnel and H.-B. Rademacher, Conformal transformations of pseudo-Riemannian manifolds, in:
  Recent developments in pseudo-Riemannian geometry (D.Alekseevsky and H.Baum, eds.),
  ESI Lectures in Mathematics and Physics, 261-298, European Math. Society 2008
• T.F. Banchoff and W. Kühnel, Tight submanifolds, smooth and polyhedral, in: Tight and taut submanifolds
  (T.E. Cecil and S.-s. Chern, eds.), MSRI Publications Vol. 32, pp. 51-118, Cambridge University Press 1997
• T. E. Cecil and W. Kühnel, Bibliography on tight, taut and isoparametric submanifolds, ibid. pp. 307-339
• W. Kühnel, Tight polyhedral submanifolds and tight triangulations, 122 p., Lecture Notes in Mathematics
  Vol. 1612, Springer 1995
• W. Kühnel, Triangulations of manifolds with few vertices, Advances in Differential Geometry and Topology
  (F. Tricerri, ed.), pp. 59-114, Proceedings of a workshop at the Institute for Scientific Interchange (Torino, Italy),
  World Scientific Publ. 1990

On the Differential Geometry of Submanifolds:

• W. Kühnel and G. Solanes, Tight surfaces with boundary, Bulletin London Math. Soc. 43, 151-163 (2011)
• M. Steller, A Gauss-Bonnet formula for metrics with varying signature, Z. Anal. Anw. 25, 143-162 (2006)
• W. Kühnel and M. Steller, On closed Weingarten surfaces, Monatsh. Math. 146, 113-126 (2005)
• F. Dillen and W. Kühnel, Total curvature of complete submanifolds of Euclidean space,
  Tôhoku Math. J. 57, 171-200 (2005)
• M.-O. Otto, Tight surfaces in three-dimensional compact Euclidean space forms,
  Transactions Amer. Math. Soc. 355, 4847-4863 (2003)
• G. Preissler, Isothermic surfaces and Hopf cylinders, Beiträge Algebra Geom. 44, 1--8 (2003)
• G. Preissler, On a generalization of Willmore surfaces for hypersurfaces, Res. Math. 35, 314--324 (1999)
• F. Dillen and W. Kühnel, Ruled Weingarten surfaces in Minkowski $3$-space,
  manuscripta math. 98, 307-320 (1999)
• M. van Gemmeren, Tightness of manifolds with $H$-spherical ends, Compositio Math. 112, 17-32 (1998)
• P. Breuer and W. Kühnel, The tightness of tubes, Forum Math. 9, 707-720 (1997)
• M. Becker and W. Kühnel, Hypersurfaces with constant inner curvature of the second fundamental form,
  and the non-rigidity of the sphere, Math. Z. 223, 693-708 (1996)
• M. van Gemmeren, Total absolute curvature and tightness of noncompact manifolds,
  Transactions Amer. Math. Soc. 348, 2413-2426 (1996)
• W. Kühnel, Ruled $W$-surfaces, Arch. Math. 62, 475-480 (1994)
• W. Kühnel, Tightness, torsion, and tubes, Ann. Global Analysis and Geometry 10, 227-236 (1992)
• W. Kühnel and U. Pinkall, On total mean curvatures, Quart. J. Math. Oxford (2) 37, 437-447 (1986)
• W. Kühnel and U. Pinkall, Tight smoothing of some polyhedral surfaces, in:
  Global Differential Geometry and Global Analysis, Proceedings Berlin 1984 (D. Ferus et al., eds.), 227-239,
  Lecture Notes in Mathematics 1156, Springer 1985
• W. Kühnel and T.F. Banchoff, The $9$-vertex complex projective plane,
  The Math. Intelligencer Vol. 5 issue 3, 11-22 (1983)
• U. Brehm and W. Kühnel, Smooth approximation of polyhedral surfaces regarding curvatures,
  Geometriae Dedicata 12, 435-461 (1982)
• W. Kühnel, Zur inneren Krümmung der zweiten Grundform, Monatsh. Math. 91, 241-251 (1981)
• W. Kühnel, $(n-2)$-tightness and curvature of submanifolds with boundary,
  Intern. J. Math. Math. Sci. 1, 421-431 (1978)

On (semi-)Riemannian Geometry and Math. Physics:

• W. Kühnel and H.-B. Rademacher, Conformally Einstein product spaces,
  Diff. Geom. Appl. 49, 65--96 (2016)
• F. Leitner and A. Rod Gover, A class of compact Poincare-Einstein manifolds: properties and construction}, Comm. Contemp. Math. 12, 629--659 (2010)
• W. Kühnel and H.-B. Rademacher, Einstein spaces with a conformal group,
  Res. Math. 56, 421-444 (2009)
• A. Rod Gover and F. Leitner, A sub-product construction of Poincare-Einstein metrics,
  Intern. J. Math. 20, 1264-1287 (2009)
• F. Leitner, Conformal holonomy of bi-invariant metrics, Conform. Geom. Dyn. 12, 18-31 (2008)
• W. Kühnel and H.-B. Rademacher, Liouville's theorem in conformal geometry, J. Math. Pures et Appl. (9) 88, 251-260 (2007),
  ESI Preprint 1862 (2006) (Erwin-Schrödinger-Institut Wien), see ESI Preprints
• F. Leitner, Twistor spinors with zero on Lorentzian 5-space, Comm. Math. Phys. 275, 587-605 (2007)
• F. Leitner, On transversally symmetric pseudo-Einstein and Fefferman-Einstein spaces,
  Math. Z. 256, 443-459 (2007)
• F. Leitner, About Complex structures in conformal tractor calculus,
  ESI Preprint 1730 (2005) (Erwin-Schrödinger-Institut Wien), see ESI Preprints
• M. Steller, Conformal vector fields on spacetimes, Annals Glob. Analysis Geom. 29, 293-317 (2006)
• W. Kühnel and H.-B. Rademacher, Conformal geometry of gravitational plane waves,
  Geometriae Dedicata 109, 175-188 (2004)
• W. Kühnel and H.-B. Rademacher, Conformal Ricci collineations of space-times,
  Gen. Relativity and Gravitation 33, 1905-1914 (2001)
• W. Kühnel and H.-B. Rademacher, Asymptotically Euclidean ends of Ricci flat manifolds, and conformal inversions,
  Math. Nachrichten 219, 125-134 (2000)
• W. Kühnel and H.-B. Rademacher, Asymptotically Euclidean manifolds and twistor spinors,
  Commun. Math. Phys. 196, 67-76 (1998), Corr. ibid. 207, 735 (1999)
• W. Kühnel and H.-B. Rademacher, Twistor spinors on conformally flat manifolds,
  Illinois J. Math. 41, 495-503 (1997)
• W. Kühnel and H.-B. Rademacher, Oscillator and pendulum equation on pseudo-Riemannian spaces,
  Tôhoku Math. J. 48, 601-612 (1996)
• W. Kühnel and H.-B. Rademacher, Twistor spinors and gravitational instantons,
  Lett. Math. Phys. 38, 411-419 (1996)
• W. Kühnel and H.-B. Rademacher, Essential conformal fields in pseudo-Riemannian geometry,
  J. Math. Pures et Appl. (9) 74, 453-481 (1995), Part II in: J. Math. Sci. Univ. Tokyo 4, 649-662 (1997)
• W. Kühnel and H.-B. Rademacher, Conformal diffeomorphisms preserving the Ricci tensor,
  Proc. Amer. Math. Soc. 123, 2841-2848 (1995)
• W. Kühnel and H.-B. Rademacher, Twistor spinors with zeros, Intern. J. Math. 5, 877-895 (1994)

On Discrete and Combinatorial Geometry and Topology:

• R. Grunert, W. Kühnel and G. Rote, PL Morse theory in low dimensions, Advances in Geometry 23, 135-150 (2023), Preprint
  
• U. Brehm and W. Kühnel, Lattice triangulations of $E3$ and of the 3-torus, Israel J. Math. 189, 97--133 (2012)
• J. Spreer, Partitioning the triangles of the cross polytope into surfaces, Beitr. Algebra und Geom. 53, 473--486 (2012)
• J. Spreer and W. Kühnel, Combinatorial properties of the K3 surface: simplicial blowups and slicings,
  Experimental Math. 20, 201-216 (2011)
• J. Spreer, Normal surfaces as combinatorial slicings, Discrete Math. 311, 1295--1309 (2011)
• F. Effenberger, Stacked polytopes and tight triangulations of manifolds, J. Comb. Th. (A) 118, 1843-1862 (2011)
• F. Effenberger and W. Kühnel, Hamiltonian submanifolds of regular polytopes ,
  Discrete Comput. Geom. 43, 242--262 (2010)
• U. Brehm and W. Kühnel, Equivelar maps on the torus, European J. Combinatorics 29, 1843-1861 (2008)
• T.F. Banchoff and W. Kühnel, Tight polyhedral models of isoparametric families, and PL--taut submanifolds ,
  Advances Geom. 7, 613-629 (2007)
• J. Itoh and W. Kühnel, Tightness of Graphs: Realizations with the Two-Piece Property,
  Rev. Roum. Math. Pures Appl. 51, 1-19 (2006)
• W. Kühnel, Tight embeddings of simply connected 4-manifolds, Documenta Math. 9, 401-412 (2004) (electronic)
• M. Casella and W. Kühnel, A triangulated K3 surface with the minimum number of vertices,
  Topology 40, 753-772 (2001)
• G. Lassmann and E. Sparla, A classification of centrally-symmetric and cyclic $12$-vertex triangulations of $S2x\; S2$,
  Discrete Math. 223, 175-187 (2000)
• W. Kühnel and F. H. Lutz, A census of tight triangulations, Periodica Math. Hungarica 39, 161-183 (1999)
• E. Sparla, A new lower bound theorem for combinatorial $2k$-manifolds,
  Graphs and Combinatorics 15, 109-125 (1999)
• E. Sparla, An upper and a lower bound theorem for combinatorial $4$-manifolds,
  Discrete Comp. Geom. 19, 575-593 (1998)
• W. Kühnel, Topological aspects of twofold triple systems, Expositiones Math. 16, 289-331 (1998)
• W. Kühnel and G. Lassmann, Permuted difference cycles and triangulated sphere bundles,
  Discrete Math. 162, 215-227 (1996)
• U. Brehm, W. Kühnel and E. Schulte, Manifold structures on abstract regular polytopes,
  Aequationes math. 49, 12-35 (1995)
• W. Kühnel, Manifolds in the skeletons of convex polytopes, tightness, and generalized Heawood inequalities,
  Polytopes: Abstract, Convex and Computational, (T. Bisztriczky et al., eds.), pp. 241-247,
  Proc. NATO Advanced Study Institute (ASI) Ser. C Vol. 440, Kluwer 1994
• T.F. Banchoff and W. Kühnel, Equilibrium triangulations of the complex projective plane,
  Geometriae Dedicata 44, 313-333 (1992)
• U. Brehm and W. Kühnel, $15$-vertex triangulations of an $8$-manifold, Math. Annalen 294, 167-193 (1992)
• W. Kühnel and G. Lassmann, Combinatorial $d$-tori with a large symmetry group,
  Discrete Comput. Geom. 3, 169-176 (1988)
• U. Brehm and W. Kühnel, Combinatorial manifolds with few vertices, Topology 26, 465-473 (1987)
• W. Kühnel, Minimal triangulations of Kummer varieties, Abh. Math. Sem. Univ. Hamburg 57, 7-20 (1987)
• W. Kühnel and G. Lassmann, Neighborly combinatorial 3-manifolds with dihedral automorphism group,,
  Israel J. Math. 52, 147-166 (1985)
• W. Kühnel and G. Lassmann, The rhombidodecahedral tessellation of 3-space and a particular
  15-vertex triangulation of the 3-dimensional torus, manuscripta math. 49, 61-77 (1984)
• W. Kühnel and G. Lassmann, The unique $3$-neighborly $4$-manifold with few vertices,
  J. Comb. Th. (A) 35, 173-184 (1983)
• W. Kühnel, Tight and $0$-tight polyhedral embeddings of surfaces, Inventiones math. 58, 161-177 (1980)

Related papers by other people on particular triangulations and conjectures:

• B. Morin and M. Yoshida, The Kühnel triangulation of the complex projective plane from the view-point
  of complex crystallography, Part I, Memoirs Fac. Sci. Kyushu Univ., Ser. A 45, 55-142 (1991)
• P. Arnoux and A. Marin, The Kühnel triangulation of the complex projective plane from the view-point
  of complex crystallography, Part II, Memoirs Fac. Sci. Kyushu Univ., Ser. A 45, 167 - 244 (1991)
• B. Bagchi and B. Datta, On Kühnel's $9$-vertex complex projective plane, Geom. Dedicata 50, 1 - 13 (1994)
• B. Bagchi and B. Datta, Minimal triangulations of sphere bundles over the circle, J. Comb. Th. A 115, 737 - 752 (2008)
• I. Novik, Upper bound theorems for homology manifolds, Israel J. Math. 108, 45-82 (1998)
• I. Novik, On face numbers of manifolds with symmetry, Advances in Math., 192, 183-208 (2005).
• J. Chestnut, J. Sapir and Ed Swartz, Enumerative properties of triangulations of spherical bundles over $S1$,
  European J. Combin. 29, 662-671 (2008),
• Ed Swartz, Face enumeration: From spheres to manifolds, J. European Math. Soc. 11, 449-485 (2009),
  see also http://www.math.cornell.edu/~ebs/papers.html