Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 39, No. 2, pp. 329-348 (1998)

Higher Order Codazzi Tensors on Conformally Flat Spaces

H. L. Liu, U. Simon, C. P. Wang

Technische Universität Berlin, MA 8-3, Strasse des 17. Juni 136, D-10623 Berlin, e-mail: /

Department of Mathematics, Beijing University, Beijing 100871, P. R. China, e-mail:

Abstract: We generalize the concept of Codazzi tensors to higher order tensors and present examples. We derive second order PDE's of Weitzenboeck type and give local and global applications to hypersurfaces in space forms, minimal submanifolds and affine hypersurfaces.

Keywords: Codazzi tensors of higher order, conformally flat spaces, Weitzenboeck formulas, affine hypersurfaces, minimal submanifolds in spheres

Classification (MSC91): 53B21, 53A15, 53A30, 53B20, 53B25, 53C20, 53C21, 53C40, 53C42

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