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

2012/03/21 by Dobrinka Gribacheva, Gribacheva, Dobrinka, Dimitar Mekerov +1
Mathematics · Physics and Astronomy · #53C05 #53C15 #53C25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1203.4682

openalex publication_date 2012/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Kähler 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 Kähler tensors in Hermitian geometry.

Related

• Natural connections on conformal Riemannian P-manifolds
• A natural connection on a basic class of Riemannian product manifolds
• Curvature relations in almost product manifolds
• Three-dimensional Riemannian manifolds associated with locally conformal Riemannian product manifolds
• Quarter-symmetric connection on an almost Hermitian manifold and on a Kähler manifold