Related papers: Almost Kenmotsu Manifolds Admitting Certain Critic…
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…
In this paper we characterize certain class of almost Kenmotsu metrics satisfying the Miao-Tam equation.
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…
In the present paper, we characterize a class of almost Kenmotsu manifolds admitting quasi Yamabe soliton. It is shown that if a $(k,\mu)'$-almost Kenmotsu manifold admits a quasi Yamabe soliton $(g,V,\lambda,\alpha)$ with $V$ pointwise…
We study $\mathcal D$-homothetic deformations of almost $\alpha$-Kenmotsu structures. We characterize almost contact metric manifolds which are $CR$-integrable almost $\alpha$-Kenmotsu manifolds, through the existence of a canonical linear…
The aim of this paper is characterize a class of contact metric manifolds admitting $\ast$-conformal Ricci soliton. It is shown that if a $(2n + 1)$-dimensional $N(k)$-contact metric manifold $M$ admits $\ast$-conformal Ricci soliton or…
We study the space of smooth Riemannian structures on compact three-manifolds with boundary that satisfies a critical point equation associated with a boundary value problem, for simplicity, Miao-Tam critical metrics. We provide an estimate…
The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting Ricci-Yamabe soliton. It is shown that a $(k,\mu)'$-almost Kenmotsu manifold admitting a Ricci-Yamabe soliton or gradient Ricci-Yamabe…
The author is planning if possible classify all three-dimensional $(\kappa,\mu)$-manifolds wether contact metric, almost cosymplectic, para-contact metric, almost para-cosymplectic. Of course classification in contact or almost cosymplectic…
The interest of mathematicians in metric $f$-manifolds, in particular, almost contact metric manifolds, is motivated by the study of the geometry and dynamics of contact foliations, as well as their applications in physics. Weak metric…
We study critical metrics of the curvature functional $\A(g)=\int_M |R|^2\, \vol$, on complete four-dimensional Riemannian manifolds $(M,g)$ with finite energy, that is, $\A(g)<\infty$. Under the natural inequality condition on the…
A dualistic structure on a smooth Riemaniann manifold $M$ is a triple $(M,g,\nabla)$ with $g$ a Riemaniann metric and $\nabla$ an affine connection, generally assumed to be torsionless. From $g$ and $\nabla$, the dual connection $\nabla^*$…
This paper applies the Newman-Penrose formalism-a technique primarily used in General Relativity-to the analysis of three-dimensional almost contact metric (ACM) manifolds. We reformulate and discuss several known notions and properties…
In this paper the notion of quasi-isometry between two Riemannian manifolds has been introduced. This idea is also imposed to study quasi-isometry between two almost contact metric manifolds. Moving further, some curvature properties of two…
Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the $(m,\rho)$-quasi-Einstein structure on a contact metric manifold. First, we prove that if…
The vector space of the tensors $\mathcal F$ of type (0,3) having the same symmetries as the covariant derivative of the fundamental form of an almost contact metric manifold is considered. A scheme of decomposition of $\mathcal F$ into…
In this article, we study an almost contact metric structure on a $G_2$-manifold constructed by Arikan, Cho and Salur in via the classification of almost contact metric structures given by Chinea and Gonzalez. In particular, we characterize…
Almost paracontact Riemannian manifolds of the lowest dimension are studied, whose paracontact distributions are equipped with an almost paracomplex structure. These manifolds are constructed as a product of a real line and a 2-dimensional…
In the present paper, we characterize almost Kenmotsu manifolds admitting holomorphically planar conformal vector (HPCV) fields. We have shown that if an almost Kenmotsu manifold $M^{2n+1}$ admits a non-zero HPCV field $V$ such that $\phi V…
In this paper, we study a general almost Schur Lemma on pseudo-Hermitian (2n+1)-manifolds $(M,J,\theta)$ for $n\geq2$. When the equality of almost Schur inequality holds, we derive the contact form $\theta$ is pseudo-Einstein and the…