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Generalized spherical functions on projectively flat manifolds

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Local and global properties of the first order spherical functions are generalized to projectively flat manifolds.

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References

  1. M. Berger, P. Gauduchon, and E. Mazet. Le spectre d’une variété Riemannienne. Lecture Notes in Mathematics 194. Springer-Verlag, Berlin, 1971.

    Google Scholar 

  2. L. P. Eisenhart. Non-Riemannian Geometry, volume VIII of Colloquium Publications. AMS, 1927.

  3. S. Kobayashi and K. Nomizu. Foundations of differential geometry, volume I. John Wiley & Sons, New York, 1963.

    MATH  Google Scholar 

  4. K. Nomizu and U. Pinkall. On a certain class of homogeneous projectively flat manifolds. Tôhoku Math. J., 39:407–427, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  5. K. Nomizu and U. Pinkall. On the geometry of affine immersions. Math. Z., 195:165–178, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  6. 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.

  7. M. Obata. Certain conditions for a Riemannian manifolds to be isometric with a sphere. J. Math. Soc. Japan, 14:333–340, 1962.

    Article  MathSciNet  MATH  Google Scholar 

  8. 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.

    MathSciNet  MATH  Google Scholar 

  9. U. Pinkall, A. Schwenk-Schellschmidt, and U. Simon. Geometric methods for solving Codazzi and Monge-Ampère equations. Math. Annalen, 298:89–100, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. A. Schouten. Ricci-Calculus. Springer-Verlag, Berlin, 2nd edition, 1954.

    MATH  Google Scholar 

  11. U. Simon. Transformation techniques for partial differential equations on projectively flat manifolds. Results in Mathematics, this volume, 1994.

  12. 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].

  13. 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.

    MathSciNet  MATH  Google Scholar 

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Dedicated to Katsumi Nomizu

Partially supported by the exchange-program UNC-TUB and by NSF grants DMS-9204942 and 9409037

Partially supported by the DFG-project Si 163/4-1

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Gardner, R.B., Kriele, M. & Simon, U. Generalized spherical functions on projectively flat manifolds. Results. Math. 27, 41–50 (1995). https://doi.org/10.1007/BF03322268

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