arXiv subjects

Mohd. Danish Siddiqi

Publications and source records attributed to Mohd. Danish Siddiqi.

5 recordsLinked to original sources

arXiv2023

Solitonic aspects of submanifolds in Kenmotsu statistical manifolds

The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In fact, its statistical counterpart, that is, Kenmotsu statistical manifold also has same importance as that of Kenmotsu manifold. Theoretical physicists have also been looking into the equation of Ricci soliton and Yamabe soliton in relation with Einstein manifolds, quasi-Einstein manifolds and string theory. In this research article, first we examine the statistical solitons and Yamabe soliton on Kenmotsu statistical manifolds with some related examples. Then we investigate some statistical curvature properties of Kenmotsu statistical manifolds. Also, we study the statistical solitons on submanifolds of Kenmotsu statistical manifold with concircular vector field. Furthermore, we discuss the behavior of almost quasi-Yamabe soliton on submanifolds of Kenmotsu statistical manifolds endowed with concircular vector field and concurrent vector filed. Finally, we furnish an example of $5$-dimensional Kenmotsu statistical manifolds admitting a statistical soliton and almost quasi-Yamabe soliton as well in the support of this study.

math.DG↗

arXiv2023

Sharp inequalities and solitons for statistical submersions

In this research article, initially, we prove some sharp inequalities on statistical submersions involving Ricci and scalar curvatures of the statistical manifolds. In addition, we establish the geometrical bearing on statistical submersions in terms of Ricci-Bourguignon soliton. Moreover, we characterize the fibers of a statistical submersion as Ricci-Bourguignon solitons with conformal vector field. Finally, in the particular case when the vertical potential vector field of the Ricci-Bourguignon soliton is of gradient type, we derive a Poisson equation for a statistical submersion.

math.DG↗

arXiv2021

$\ast$-$η$-Ricci-Yamabe solitons on $α$-Cosymplectic manifolds with a quarter-symmetric metric connection

The goal of the present paper is to deliberate certain types of metric such as $*$-$η$-Ricci-Yamabe soliton on $α$-Cosymplectic manifolds with respect to quarter-symmetric metric connection. Further, we have proved some curvature properties of $α$-Cosymplectic manifolds admitting quarter-symmetric metric connection. Here, we have shown the characteristics of the soliton when the manifold satisfies quarter-symmetric metric connection on $α$-Cosymplectic manifolds. Later, we have acquired Laplace equation from $*$-$η$-Ricci-Yamabe soliton equation when the potential vector field $ξ$ of the soliton is of gradient type in terms of quarter-symmetric metric connection. Next, we have developed the nature of the soliton when the vector field is conformal killing admitting quarter-symmetric metric connection. Finally, we present an example of a 5-dimensional $α$-cosymplectic metric as a $*$-$η$-Ricci-Yamabe soliton with respect to a quarter-symmetric metric connection to prove our results.

math.DG↗

arXiv2020

$η$-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds

In this research article, we establish the geometrical bearing on Riemannian submersions in terms of $η$-Ricci-Yamabe Soliton with the potential field and giving the classification of any fiber of Riemannian submersion is an $η$-Ricci-Yamabe soliton, $η$-Ricci soliton and $η$-Yamabe soliton. We also discuss the various conditions for which the target manifold of Riemannian submersion is an $η$-Ricci-Yamabe soliton, $η$-Ricci soliton, $η$-Yamabe soliton and quasi-Yamabe soliton. In a particular case when the potential filed $V$ of the $η$-Ricci-Yamabe soliton is of gradient type, we derive a Laplacian equation and providing some examples of an $η$-Ricci-Yamabe soliton on a Riemannian submersion. Finally, we study harmonic aspect of $η$-Ricci-Yamabe soliton on Riemannian submersions and mention geometrical and physical effects of Ricci-Yamabe solitons.

math.DG↗

arXiv2018

$η$- Ricci Solitons on Kenmotsu manifold with Generalized Symmetric Metric Connection

The objective of the present paper is to study the $η$-Ricci solitons on Kenmotsu manifold with generalized symmetric metric connection of type $(α,β)$. There are discussed Ricci and $η$-Ricci solitons with generalized symmetric metric connection of type $(α,β)$ satisfying the conditions $\bar{R}.\bar{S}=0$, $\bar{S}.\bar{R}=0$, $\bar{W_{2}}.\bar{S}=0$ and $\bar{S}.\bar{W_{2}}=0.$. Finally, we construct an example of Kenmotsu manifold with generalized symmetric metric connection of type $(α,β)$ admitting $η$-Ricci solitons.

math.DG↗