Extended Derdzinski-Shen theorem for the Riemann tensor

Details Extended Derdzinski-Shen theorem for the Riemann tensor Extended Derdzinski-Shen theorem for the Riemann tensor

2011-01-21

arxiv.org/abs/1101.4157v1

Mathematics

Differential Geometry

5 pages

Scientific paper

We extend a classical result by Derdzinski and Shen, on the restrictions
imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor.
The new conditions of the theorem include Codazzi tensors (i.e. closed 1-forms)
as well as tensors with gauged Codazzi condition (i.e. "recurrent 1-forms"),
typical of some well known differential structures.

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