/pdf/isometry-of-kaehlerian-manifolds-to-complex-projective-ju5ihqh3hz.pdf

Integral formulas in riemannian geometry

Isometry of Kaehlerian manifolds to complex projective spaces

/pdf/killing-vector-fields-on-non-compact-riemannian-manifolds-b5y5npmw0b.pdf

Killing vector fields on non-compact Riemannian manifolds with boundary

The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton then it is isometric to a unit sphere S2n+1. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci soliton where the potential vector field X is point wise collinear with the Reeb vector field {\xi} of the contact metric structure.

The $k$-almost Ricci solitons and contact geometry

Some characterizations of ρ-Einstein solitons

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 $\lambda$ is zero. For 3-dimensional case, if $M$ admits a $*$-Ricci soliton, then we show that $M$ is of constant sectional curvature -1. Next, we show that if $M$ admits a $*$-Ricci soliton whose potential vector field is collinear with the characteristic vector field $\xi$, then $M$ is Einstein and soliton vector field is equal to $\xi$. Finally, we prove that if $g$ is a gradient almost $*$-Ricci soliton, then either $M$ is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of $M$. We verify our result by constructing examples for both $*$-Ricci soliton and gradient almost $*$-Ricci soliton.

Integral formulas in riemannian geometry

Citations

Isometry of Kaehlerian manifolds to complex projective spaces

Killing vector fields on non-compact Riemannian manifolds with boundary

The $k$-almost Ricci solitons and contact geometry

Some characterizations of ρ-Einstein solitons

$$-Ricci solitons and gradient almost $$-Ricci solitons on Kenmotsu manifolds

Related Papers (5)

Riemannian Geometry of Contact and Symplectic Manifolds

The entropy formula for the Ricci flow and its geometric applications

Certain conditions for a Riemannian manifold to be isometric with a sphere

A class of almost contact riemannian manifolds

Curvature and Betti numbers

Integral formulas in riemannian geometry

Citations

Isometry of Kaehlerian manifolds to complex projective spaces

Killing vector fields on non-compact Riemannian manifolds with boundary

The $k$-almost Ricci solitons and contact geometry

Some characterizations of ρ-Einstein solitons

$*$-Ricci solitons and gradient almost $*$-Ricci solitons on Kenmotsu manifolds

Related Papers (5)

Riemannian Geometry of Contact and Symplectic Manifolds

The entropy formula for the Ricci flow and its geometric applications

Certain conditions for a Riemannian manifold to be isometric with a sphere

A class of almost contact riemannian manifolds

Curvature and Betti numbers

$$-Ricci solitons and gradient almost $$-Ricci solitons on Kenmotsu manifolds