arXiv research

Study properties of Kenmotsu manifolds with conformal η-Einstein soliton metrics.

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $\varphi$-sectional curvature, and prove the structure theorem for $ξ$-conformally fla…

The aim of the present paper is to study the properties of Kenmotsu manifolds equipped with a non-symmetric non-metric connection. We also establish some curvature properties of Kenmotsu manifolds. It is proved that a Kenmotsu manifold endowed with a non-symmetric non-metric is irregular.

In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds. Later, such a manifold was called a Kenmotsu manifold. This paper, we studied Kenmotsu manifolds with $(2n+s)$-dimensional $s-$contact metric manifold and this manifold, we have called generalized Kenmotsu manifolds. Necessary and sufficient c…

The paper explores $*$-conformal $η$-Ricci solitons in Kenmotsu manifolds.

The paper characterizes Kenmotsu metrics as almost $*$-Ricci solitons.

The paper characterizes Einstein metrics in Kenmotsu manifolds using specific soliton types.

In this paper, we have studied the critical point equation (shortly, CPE) within the frame-work of Kenmotsu and almost Kenmotsu manifold satisfying certain nullity conditions. First, we prove that a complete Kenmotsu metric satisfies the CPE is Einstein and locally isometric to the hyperbolic space H2n+1. In case of Ke…

Study $\ast$-$η$-Ricci solitons on weak Kenmotsu $f$-manifolds.

In this paper we characterize certain class of almost Kenmotsu metrics satisfying the Miao-Tam equation.

Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.

Study of $η$-Ricci solitons and $η$-Einstein metrics on weak $β$-Kenmotsu $f$-manifolds.

The paper studies critical metrics on a specific type of manifold.

The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-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}.\…

The paper characterizes Kenmotsu manifolds with conformal η-Ricci solitons.

The paper characterizes a class of almost Kenmotsu manifolds with quasi Yamabe solitons.

Study on Schouten solitons on Kenmotsu manifolds, focusing on torse-forming vector fields.

The paper characterizes specific almost Kenmotsu manifolds with Ricci-Yamabe solitons.

We study $\mathcal D$-homothetic deformations of almost $α$-Kenmotsu structures. We characterize almost contact metric manifolds which are $CR$-integrable almost $α$-Kenmotsu manifolds, through the existence of a canonical linear connection, invariant under $\mathcal D$-homothetic deformations. If the canonical connect…

The present paper deals with the study of pseudo parallel (in the sense of Chaki and in the sense of Deszcz) contact CR-submanifolds with respect to Levi-Civita connection as well as semisymmetric metric connection of Kenmotsu manifolds and prove that these corresponding two classes are equivalent with a certain condit…

The present study initially identified the generalized symmetric connections $(α,β)$ typed, which can be regarded as more generalised forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively particularly when $(α,β)=(1,0)$ and $(α,β)=(0,1)$ are taken into con…

We study the Riemann curvature tensor of (κ,μ,ν)-spaces when they have almost cosymplectic and almost Kenmotsu structures, giving its writing explicitly. This leads to the definition and study of a natural generalisation of the contact metric (κ,μ,ν)-spaces. We present examples or obstruction results of these spaces in…

The study examines Riemann solitons and almost solitons on specific Kenmotsu manifolds.

This is an expository paper, which provides a first approach to nearly Kenmotsu manifolds. The purpose of this paper is to focus on nearly Kenmotsu manifolds and get some new results from it. We prove that for a nearly Kenmotsu manifold is locally isometric to warped product of real line and nearly Kähler manifold. Fin…

Study of $η$-Ricci solitons on Kenmotsu 3-manifolds.

The paper characterizes $\ast$-Ricci-Bourguignon solitons on Kenmotsu manifolds.

In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we investigate further properties of invariant submanifolds of \ a generalized Kenmotsu man…

Study finds specific Lie groups with Kenmotsu structures.

A structure on an almost contact metric manifold is defined as a generalization of well-known cases: Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic. Then we consider a semi-invariant $ξ^{\bot}$-submanifold of a manifold endowed with such a structure and two topics are studied: the integrability of distributions de…

Kenmotsu geometry is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In this article, we study the statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properti…

Study on triharmonic curves in f-Kenmotsu 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 b…

In this paper we study para-Kenmotsu manifolds. We characterize this manifolds by tensor equations and study their properties. We are devoted to a study of $η-$Einstein manifolds. We show that a conformally flat para-Kenmotsu manifold is a space of constant negative curvature $-1$ and we prove that if a para-Kenmotsu m…

As a generalization of slant submanifolds and semi-slant submanifolds, we introduce the notions of pointwise slant submanifolds and pointwise semi-slant sunmanifolds of an almost contact metric manifold. We obtain a characterization at each notion, investigate the topological properties of pointwise slant submanifolds,…

The paper studies a new soliton on Kenmotsu manifolds and derives its scalar curvature.

For a finite family of 3-dimensional almost contact metric manifolds with closed the structure form $η$ is described a construction of an almost contact metric manifold, where the members of the family are building blocks - cells. Obtained manifold share many properties of cells. One of the more important are nullity c…

Characterizes $*$-$k$-Ricci-Yamabe solitons on Kenmotsu manifolds.

The study characterizes almost Kenmotsu manifolds with specific vector fields.

In this paper, we consider $*$-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if the metric of a Kenmotsu manifold $M$ is a $*$-Ricci soliton, then soliton constant $λ$ is zero. For 3-dimensional case, if $M$ admits a $*$-Ricci soliton, then we show that $M$ is of constant sectional curvatu…

Study constructs Frenet curves using semi-symmetric metric connection.

In the present paper, we study warped product semi-slant submanifolds of Kenmotsu manifolds. We have obtained results on the existence of warped product semi-slant submanifolds of Kenmotsu manifolds in term of the canonical structure .

The paper studies bi-slant Riemannian maps to Kenmotsu manifolds and derives inequalities.

In this paper, we investigate the condition on warped product manifold of a Kenmotsu manifold and the real line to be a conformal Kahler manifold. This result demonstrates the close relation of Kenmotsu and Kahler manifolds.

Study on solitons in deformed Kenmotsu manifolds with specific vector fields.

The study examines almost Ricci-Yamabe solitons on almost Kenmotsu manifolds and their properties.

The Eisenhart problem of finding parallel tensors is solved for the symmetric case in the regular $f$-Kenmotsu framework. On this way, the Olszack-Rosca example of Einstein manifolds provided by $f$-Kenmotsu manifolds via locally symmetric Ricci tensors is recovered as well as a case of Killing vector fields. Some othe…

We introduce a new general class of metric f-manifolds which we call (nearly) trans-S-manifolds and includes S- manifolds, C-manifolds, s-th Sasakian manifolds and generalized Kenmotsu manifold studied previously. We prove their main properties and we present many examples which justify their study.