Work

Weakly B-Symmetric Warped Product Manifolds with Applications

Year: 2025

Type: article

Abstract: This work presents a comprehensive study of weakly B-symmetric warped product manifolds (WBS)n, a natural extension of several classical curvature-restricted geometries including B-flat, B-parallel, and B-recurrent manifolds. We begin by formulating the fundamental properties of the B-tensor B(X,Y)=aS(X,Y)+brg(X,Y), where S is the Ricci tensor, r the scalar curvature, and a,b are smooth non-vanishing functions. The warped product structure is then exploited to obtain explicit curvature identities for base and fiber manifolds under various geometric constraints. Detailed characterizations are established for Einstein conditions, Codazzi-type tensors, cyclic parallel tensors, and the behavior of geodesic vector fields. The weakly B-symmetric condition is analyzed through all possible projections of vector fields, leading to sharp criteria describing the interaction between the warping function and curvature. Several applications are discussed in the context of Lorentzian geometry, including perfect fluid and generalized Robertson–Walker spacetimes in general relativity. These results not only unify different curvature-restricted frameworks but also reveal new geometric and physical implications of warped product manifolds endowed with weak B-symmetry.

Source: Axioms

DOI: 10.3390/axioms14100749

Authors: Bang-Yen Chen, Sameh Shenawy, Uday Chand De, Safaa Ahmed, Hanan Alohali

Institutions: Michigan State University, Modern Academy for Engineering and Technology, University of Calcutta, Fayoum University, King Saud University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: King Saud University