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The Structure Of Certain Riemannian Manifolds Admitting Codazzi Tensors by Andrzej Ge̖barowski is a Mathematics article available to read on EtoBox.

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on a Riemannian manifold M is said to be a Codazzi tensor if it satisfies the Codazzi equation for arbitrary vector fields u, v, w. Given a Codazzi tensor A on a Riemannian manifold M, let MA denote the set of all points p of M such that A in a neighbourhood of p has differentiate eigenvalue functions of constant multiplicities. Thus, MA is a dense open subset of M. The tangent bundle of each connected component U of MA splits differentiably as the orthogonal Whitney sum of the eigenspace bundles of A. In the sequel we denote by V\ the eigenspace bundle corresponding to an eigenvalue function A and by g the metric of the Riemannian manifold M.

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Author

Andrzej Ge̖barowski

Publisher

Walter de Gruyter GmbH

Published

1994

Field

Mathematics (Physical Sciences)