Osserman and conformally Osserman manifolds with warped and twisted product structure

TL;DR

This paper characterizes Osserman and conformally Osserman Riemannian manifolds with warped and twisted product structures, showing that only constant curvature manifolds can be expressed as twisted products.

Contribution

It provides a characterization of Osserman and conformally Osserman manifolds with warped and twisted product structures, revealing that twisted product Osserman manifolds must have constant curvature.

Findings

Only constant curvature manifolds can be expressed as twisted products among Osserman manifolds.

The local structure of Osserman manifolds can be characterized via warped product structures.

Twisted product structures do not admit non-constant curvature Osserman manifolds.

Abstract

We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature.