M. Danish Siddiqi

Bio: M. Danish Siddiqi is an academic researcher. The author has contributed to research in topics: Statistical manifold & Manifold. The author has an hindex of 1, co-authored 2 publications receiving 3 citations.

Characteristics of Ricci Soliton in Kenmotsu statistical manifolds

Abstract: Kenmotsu geometry is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. Theoretical physicists have also been looking into the equation of Ricci soliton in relation with Einstein manifolds, Quasi Einstein manifolds and string theory. In this research article, we study the Ricci solitons on statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properties of Kenmotsu statistical manifolds. We prove that a Kenmotsu statistical manifold is not a Ricci-flat statistical manifold with an example. Also, we investigate $\eta$-Ricci solitons on submanifolds of Kenmotsu statistical manifold and satisfying the Ricci semi-symmetric condition. Moreover, we have also discuss the behavior of Ricci solitons in two specific cases: $(i)$ when the potential vector field $\xi$ is of gradient type, $\xi=grad(\psi)$, we derive from the Ricci soliton a Laplacian equation satisfied by $\psi$, and $(ii)$ the potential vector field $\xi$ is a torqued vector filed $\tau$, proves that Kenmotsu statistical manifold is generalized quasi-Einstein.

Study of Solitons on submanifolds of Kenmotsu statistical manifolds

Abstract: The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. 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 servey, we examine the Ricci solitons and Yamabe soliton on statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properties of Kenmotsu statistical manifolds. Also, we study the almost $\eta$-Ricci solitons on submanifolds of Kenmotsu statistical manifold with concircular vector field. Furthermore, we have also discuss the behavior of almost quasi-Yamabe soliton on subamnifolds of Kenmotsu statistical manifolds endowed with concircular vector field and concurrent vector filed. Finally, we have furnish an example of $5$-dimensional Kenmotsu statistical manifolds admitting the $\eta$-Ricci soliton and almost quasi-Yamabe soliton as well.

Hypersurfaces in Statistical Manifolds

Abstract: The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given as a first step of the statistical submanifold theory. A complex version of the notion of statistical structures is also introduced.

Eta-ricci solitons on kenmotsu manifold with generalized symmetric metric connection

Abstract: The objective of the present paper is to study the $\eta$-Ricci solitons on Kenmotsu manifold with generalized symmetric metric connection of type $(\alpha,\beta)$. There are discussed Ricci and $\eta$-Ricci solitons with generalized symmetric metric connection of type $(\alpha,\beta)$ 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 $(\alpha,\beta)$ admitting $\eta$-Ricci solitons.

Certain curvature conditions on Kenmotsu manifolds admitting a quarter-symmetric metric connection

Abstract: We study certain curvature properties of Kenmotsu manifolds with respect to the quarter-symmetric metric connection. First we consider Ricci semisymmetric Kenmotsu manifolds with respect to a quarter-symmetric metric connection. Next, we study ξ-conformally flat and ξ-concircularly flat Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Moreover, we study Kenmotsu manifolds satisfying the condition ˜Z(ξ,Y)• ˜S = 0, where ˜Z and ˜S are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Then, we prove the non-existence of ξ-projectively flat and pseudo-Ricci symmetric Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Finally, we construct an example of a 5-dimensional Kenmotsu manifold admitting a quarter-symmetric metric connection for illustration.