Invariant tensors related with natural connections for a class Riemannian product manifolds

TL;DR

This paper investigates invariant tensors associated with natural connections on specific classes of Riemannian product manifolds, enhancing understanding of their geometric properties.

Contribution

It identifies and analyzes invariant tensors linked to natural connections within two Naveira classes of Riemannian product manifolds, providing new insights into their structure.

Findings

Invariant tensors are characterized for two Naveira classes.

Relations between invariant tensors and natural connections are established.

The study advances the geometric understanding of Riemannian product manifolds.

Abstract

Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metric and the product structure.