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September 10, 2025

On Special Weakly Conharmonic Symmetric Manifolds

SKShyam KishorUniversity of Lucknow AVA. L. VermaAmity University

Key Points

The study reveals key properties of the Ricci tensor in special weakly conharmonic symmetric manifolds.
Analysis of the Ricci tensor of type (1,1) has been conducted in the context of special weakly symmetric manifolds.
Investigations highlight the distinctions in Ricci tensor properties compared to traditional symmetric manifolds.
Findings point to the implications of weakly symmetric structures in Riemannian geometry.

Abstract

The notions of a weakly symmetric and weakly projective symmetric Riemannian manifolds have been introduced by Tamassy and Binh 20, 21 and then after studied by so many authors 5, 12, 13, 14, 15, 16, 17. Recently, Singh and Khan 19 introduced the notion of Special weakly symmetric Riemannian manifolds and denoted such manifold by (SW S)n. Patra and Hui 11 generalized weakly conharmonic symmetric manifolds Kishor and Verma have investigated the properties of the Ricci tensor R of type (1,1) in special weakly M -projective symmetric manifolds 7. In this paper, we have studied the nature of Ricci tensor R of type (1,1) in a special weakly conharmonic symmetric Riemannian manifold (SW HS)n and also explored some interesting results on (SW HS)n.

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