arXiv subjects

Carlo Alberto Mantica

Publications and source records attributed to Carlo Alberto Mantica.

38 records · Page 3Linked to original sources

arXiv2011

Extended Derdzinski-Shen theorem for the Riemann tensor

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.

math.DG↗

arXiv2009

A second-order identity for the Riemann tensor and applications

A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds with Recurrent or Symmetric structures are discussed. The new structure of K-recurrency naturally emerges from an invariance property of an old identity by Lovelock.

math.DG↗