Extended Derdziński–Shen theorem for curvature tensors

Authors:

CMCarlo Alberto Mantica
Carlo Alberto Mantica
LMLuca Guido Molinari
Luca Guido Molinari

1 January 2012

journal article
Published by Institute of Mathematics, Polish Academy of Sciences in Colloquium Mathematicum

Vol. 128 (1) , 1-6
DOI:10.4064/cm128-1-1

Abstract

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.Comment: 5 page

Keywords

DIFFERENTIAL
CURVATURE
PAGE
RIEMANN
CODAZZI TENSORS
THEOREM
NONTRIVIAL
SHEN
DERDZINSKI

All Related Versions

Version 1, 2011-01-21, ArXiv