arXiv subjects

Bidhan Mondal

Publications and source records attributed to Bidhan Mondal.

3 recordsLinked to original sources

arXiv2026

K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection

In this paper, we introduce some type vector fields with respect to a semi-symmetric non-metric (SSNM) connection. We investigate several geometric properties of a K-contact manifold equipped with an SSNM connection and provide a concrete example to justify the relation between the scalar curvature of the SSNM connection and Levi-Civita connection that we have obtained in this paper. Furthermore, we have found the nature of Riemann solitons, conformal Ricci solitons and conformal $η$-Ricci-Yamabe solitons on K-contact manifolds admitting a SSNM connection.\\ Finally, we determine the necessary and sufficient conditions for such a manifold to be $\Tildeτ$-semi-symmetric, quasi-conformal-semi-symmetric and pseudo-projective-semi-symmetric.

math.DG↗

arXiv2026

Hyperbolic solitons on trans-Sasakian space forms and its submanifolds

Kong and Liu introduced the concept of hyperbolic Ricci flow in 2007 and used it to study the wave character of metrics. After that, many mathematicians have used this new geometric flow to study the evolution of manifolds and their structures. Ricci solitons and hyperbolic Ricci solitons are self-similar solitons of the Ricci flow and hyperbolic Ricci flow respectively. In this paper, we introduce the concept of hyperbolic $*-$Ricci solitons and hyperbolic Ricci-Yamabe solitons on a trans-Sasakian space forms and characterized the nature of some hyperbolic solitons. Additionally, we deduce the Ricci tensors of submanifolds of trans-Sasakian space forms and conformal trans-Sasakian space form and found the nature of solitons on submanifolds. Finally, we have included an example which will justify our result.

math.DG↗

arXiv2025

Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form

Lorantzian trans-Sasakian space form is a special type of space form in which the nature of even and odd dimensional space form both exist. Various curvature tensors with respect to Levi-Civita connection on the space form are derived in this paper. We have shown that if an odd-dimensional Lorentzian trans-Sasakian space form admits a hyperbolic Ricci soliton and hyperbolic conformal Ricci soliton then they will be $η$-Einstein. We also obtained the conditions for the solitons to be expanding, steady or shrinking. Finally, an example has been constructed which justifies the results obtained.

math.DG↗