Related papers: Sasakian Manifold and *-Ricci Tensor

The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered for the symmetric case and the result is interpreted in terms of Ricci solitons. If the…

We study eta-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem for Sasakian geometry to prove the existence of eta-Einstein…

Weak almost contact metric manifolds (i.e., the complex structure is replaced by a nonsingular skew-symmetric tensor), defined by the author and R. Wolak, allow a new look at the classical theory and find novel applications. An important…

The present paper deals with the generalized symmetric metric connection defined on para-Sasaki-like manifolds. We derive a relation between the Levi-Civita connection and the generalized symmetric metric conneciton on the considered…

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…

The goal of the current paper is to characterize $*$-$k$-Ricci-Yamabe soliton within the framework on Kenmotsu manifolds. Here, we have shown the nature of the soliton and find the scalar curvature when the manifold admitting…

$(N(k),\xi)$-semi-Riemannian manifolds are defined. Examples and properties of $(N(k),\xi)$-semi-Riemannian manifolds are given. Some relations involving ${\cal T}_{a}$-curvature tensor in $(N(k),\xi)$-semi-Riemannian manifolds are proved.…

The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci…

The present paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide some examples of such submanifolds and…

The aim of this note is to study the measure-valued Ricci tensor on smooth metric measure space with boundary, which is a generalization of Bakry-Emery's modified Ricci tensor on weighted Riemannian manifold. As an application, we offer a…

In this paper, we study several properties of Sasaki-Ricci solitons as singularity models of the Sasaki-Ricci flow. First, we establish several fundamental equations for Sasaki-Ricci solitons, which enable us to derive potential estimates…

Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $\Pi$-manifolds are studied. It is proved that these objects have constant soliton coefficients. For the soliton under study is shown that the corresponding scalar…

We extend to the Sasakian setting a result of Tian and Zhu about the decomposition of the Lie algebra of holomorphic vector fields on a K\"ahler manifold in the presence of a K\"ahler-Ricci soliton. Furthermore we apply known deformations…

The present paper is to deliberate the class of $3$-dimensional trans-Sasakian manifolds which admits $\eta$-Einstein solitons. We have studied $\eta$-Einstein solitons on $3$-dimensional trans-Sasakian manifolds where the Ricci tensors are…

The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenb\"ock formulas for the…

We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of $\eta$-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterising them in terms of generalised Killing spinors. We propose…

In this paper, we first confirm the Hamilton-Tian conjecture for the Sasaki-Ricci flow in a compact transverse Fano quasi-regular Sasakian $5$-manifold with klt foliation singularities. Secondly, we derive the compactness theorem of…

In this paper we provide a local construction of a Sasakian manifold given a K\"ahler manifold. Obatined in this way manifold we call Sasakian lift of K\"ahler base. Almost contact metric structure is determined by the operation of the lift…

Let $(g,X)$ be a Sasaki-Ricci soliton on a Sasakian manifold $S$. We prove that if $(S,g)$ admits a local Sasakian immersion in a Sasakian space form $S(N,c)$ of constant $\phi$-sectional curvature $c$, then $S$ is $\eta$-Einstein and its…

We study the properties of LP-Sasakian manifolds endowed with generalized $% \eta -$Ricci solitons associated to the general connection. Finally, the existence of such solitons on a 4-dimensional LP-Sasakian manifold is proved by…