Conformal Riemannian P-Manifolds with Connections whose Curvature Tensors are Riemannian P-Tensors

TL;DR

This paper investigates conformal Riemannian P-manifolds with special connections, exploring their curvature tensors' properties, analogous to Kähler tensors in Hermitian geometry, to deepen understanding of their geometric structure.

Contribution

It introduces properties of conformal Riemannian P-manifolds with connections whose curvature tensors resemble Kähler tensors, expanding the theory of such manifolds.

Findings

Characterization of curvature tensors in conformal Riemannian P-manifolds

Conditions under which these tensors are Riemannian P-tensors

Analogies with Kähler geometry in Hermitian manifolds

Abstract

The largest class of Riemannian almost product manifolds, which is closed with respect to the group of the conformal transformations of the Riemannian metric, is the class of the conformal Riemannian P-manifolds. This class is an analogue of the class of the conformal K\"ahler manifolds in almost Hermitian geometry. The main aim of this work is to obtain properties of manifolds of this class with connections, whose curvature tensors have similar properties as the K\"ahler tensors in Hermitian geometry.