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Preprint 604-1998

Generating higher order Codazzi tensors by functions

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Author(s) : Judith Leder, Angela Schwenk-Schellschmidt, Udo Simon, Martin Wiehe

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 604-1998

MSC 2000

53A05 Surfaces in Euclidean space
53A15 Affine differential geometry
53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions
53C40 Global submanifolds

Abstract :
We study higher order Codazzi tensors on constant curvature spaces and show how they can be generated by functions. We give applications in Riemannian geometry and hypersurface theory; in particular we characterize ellipsoids in terms of second order spherical harmonics.

Keywords : Codazzi tensors, spherical harmonics, Riemannian sphere, projective structures, quadrics

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