Codazzi Tensors and the Topology of Surfaces |
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Authors: | H. L. Liu U. Simon C. P. Wang |
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Affiliation: | (1) Department of Mathematics, Northeast University, Shenyang, 110006, China;(2) Technische Universität Berlin, MA 8-3, Straße des 17. Juni 136, D-10623 Berlin, Germany |
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Abstract: | We introduce the notion of (0,m)-Codazzi tensors relative to an affine connection which extends the well known concept for m = 2. On compact Riemannian surfaces of genus we determine the dimension of the R-vector space of traceless Codazzi tensors, which depends on m and only, additionally we extend these result for genus zero. We give some exemplary applications to submanifolds in affine and in Riemannian geometry and to Weyl geometries. |
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Keywords: | Codazzi tensor index method topologyof surfaces |
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