Geometric properties of weakly G-projectively symmetric manifolds

Abstract

The present paper is devoted to the study of weakly G-projectively symmetric
manifolds, denoted by (WGPS)n, n > 2. We first investigate several fundamental
geometric properties of these manifolds and derive conditions involving the
Ricci tensor and the associated 1-forms. We then examine the decomposability of
(WGPS)n, n > 2 manifolds and establish certain geometric characterizations. Finally,
we demonstrate the existence of such manifolds by constructing a non-trivial
example.