Generalized spherical functions on projectively flat manifolds
Article
First Online:
Received:
- 5 Downloads
- 2 Citations
Abstract
Local and global properties of the first order spherical functions are generalized to projectively flat manifolds.
MOS classification
53 B10 53 A15 33 C35Key words
spherical functions projectively flat manifoldsPreview
Unable to display preview. Download preview PDF.
References
- [BGM71]M. Berger, P. Gauduchon, and E. Mazet. Le spectre d’une variété Riemannienne. Lecture Notes in Mathematics 194. Springer-Verlag, Berlin, 1971.Google Scholar
- [Eis27]L. P. Eisenhart. Non-Riemannian Geometry, volume VIII of Colloquium Publications. AMS, 1927.Google Scholar
- [KN63]S. Kobayashi and K. Nomizu. Foundations of differential geometry, volume I. John Wiley & Sons, New York, 1963.MATHGoogle Scholar
- [NP87a]K. Nomizu and U. Pinkall. On a certain class of homogeneous projectively flat manifolds. Tôhoku Math. J., 39:407–427, 1987.MathSciNetMATHCrossRefGoogle Scholar
- [NP87b]K. Nomizu and U. Pinkall. On the geometry of affine immersions. Math. Z., 195:165–178, 1987.MathSciNetMATHCrossRefGoogle Scholar
- [NS91]K. Nomizu and U. Simon. Notes on conjugate connections. In F. Dillen and L. Verstraelen, editors, Geometry and Topology of Submanifolds, IV. Proc. Conf. Diff. Geom. Vision, pages 152-172, Leuven (Belgium), 1991. World Scientific, Singapore, 1992.Google Scholar
- [Oba62]M. Obata. Certain conditions for a Riemannian manifolds to be isometric with a sphere. J. Math. Soc. Japan, 14:333–340, 1962.MathSciNetMATHCrossRefGoogle Scholar
- [OS83]V. Oliker and U. Simon. Codazzi tensors and equations of Monge-Ampére type on compact manifolds of constant sectional curvature. J. reine angew. Math., 342:35–65, 1983.MathSciNetMATHGoogle Scholar
- [PSS94]U. Pinkall, A. Schwenk-Schellschmidt, and U. Simon. Geometric methods for solving Codazzi and Monge-Ampère equations. Math. Annalen, 298:89–100, 1994.MathSciNetMATHCrossRefGoogle Scholar
- [Sch54]J. A. Schouten. Ricci-Calculus. Springer-Verlag, Berlin, 2nd edition, 1954.MATHGoogle Scholar
- [Sim94]U. Simon. Transformation techniques for partial differential equations on projectively flat manifolds. Results in Mathematics, this volume, 1994.Google Scholar
- [SSV91]U. Simon, A. Schwenk-Schellschmidt, and H. Viesel. Introduction to the affine differential geometry of hypersurfaces. Lecture Notes. Science University of Tokyo, 1991. [Distribution TU Berlin, ISBN 3 7983 1529 9].Google Scholar
- [Tan72]K. Tandai. Riemannian manifolds admitting more than n − 1 linearly independent solutions of \(\nabla 2\rho+c 2\rho g=0\). Hokkaido Math. J., 1:12–15, 1972.MathSciNetMATHGoogle Scholar
Copyright information
© Birkhäuser Verlag, Basel 1995