scholarly journals f– Kenmotsu Metric as Conformal Ricci Soliton

2017 ◽  
Vol 55 (1) ◽  
pp. 119-127
Author(s):  
H. G. Nagaraja ◽  
K. Venu
Keyword(s):  
Ricci Soliton ◽  
Ricci Solitons ◽  
Kenmotsu Manifolds

AbstractIn this paper, we study conformal Ricci solitons in f- Kenmotsu manifolds. We derive conditions for f-Kenmotsu metric to be a conformal Ricci soliton.

scholarly journals Certain results on Ricci solitons in α-Kenmotsu manifolds

2018 ◽  
Vol 18 (1) ◽  
pp. 11-15
Author(s):  
Rajesh Kumar ◽  
Ashwamedh Mourya
Keyword(s):  
Vector Field ◽  
Ricci Soliton ◽  
Second Order ◽  
Ricci Solitons ◽  
Kenmotsu Manifold ◽  
Constant Multiple ◽  
Metric Tensor ◽  
Kenmotsu Manifolds

In this paper, we study some curvature problems of Ricci solitons in α-Kenmotsu manifold. It is shown that a symmetric parallel second order-covariant tensor in a α-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (Lvg + 2S) is parallel where V is a given vector field, then the structure (g, V, λ) yield a Ricci soliton. Further, by virtue of this result, Ricci solitons for n-dimentional α-Kenmotsu manifolds are obtained. In the last section, we discuss Ricci soliton for 3-dimentional α-Kenmotsu manifolds.

scholarly journals RICCI SOLITONS AND GRADIENT RICCI SOLITONS ON NEARLY KENMOTSU MANIFOLDS

2019 ◽  
pp. 503
Author(s):  
Gülhan Ayar ◽  
Mustafa Yıldırım
Keyword(s):  
Ricci Soliton ◽  
Ricci Solitons ◽  
Gradient Ricci Solitons ◽  
Kenmotsu Manifolds ◽  
Curvature Tensors

In this paper, we study nearly Kenmotsu manifolds with Ricci soliton and we obtain certain conditions about curvature tensors.

scholarly journals Ricci Solitons in β-Kenmotsu Manifolds

2018 ◽  
Vol 56 (1) ◽  
pp. 149-163
Author(s):  
Rajesh Kumar
Keyword(s):  
Vector Field ◽  
Ricci Soliton ◽  
Second Order ◽  
Ricci Solitons ◽  
Kenmotsu Manifold ◽  
Constant Multiple ◽  
Metric Tensor ◽  
3 Dimensional ◽  
Kenmotsu Manifolds

Abstract The object of the present paper is to study Ricci soliton in β-Kenmotsu manifolds. Here it is proved that a symmetric parallel second order covariant tensor in a β-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (ℒVg +2S)is ∇-parallel where V is a given vector field, then the structure (g, V, λ) yields a Ricci soliton. Further, by virtue of this result, we found the conditions of Ricci soliton in β-Kenmotsu manifold to be shrinking, steady and expending respectively. Next, Ricci soliton for 3-dimensional β-Kenmotsu manifold are discussed with an example.

scholarly journals Conformal $ \eta $-Ricci solitons within the framework of indefinite Kenmotsu manifolds

2022 ◽  
Vol 7 (4) ◽  
pp. 5408-5430
Author(s):  
Yanlin Li ◽  
◽  
Dipen Ganguly ◽  
Santu Dey ◽  
Arindam Bhattacharyya ◽  
...  
Keyword(s):  
Potential Function ◽  
Ricci Tensor ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds

<abstract><p>The present paper is to deliberate the class of $ \epsilon $-Kenmotsu manifolds which admits conformal $ \eta $-Ricci soliton. Here, we study some special types of Ricci tensor in connection with the conformal $ \eta $-Ricci soliton of $ \epsilon $-Kenmotsu manifolds. Moving further, we investigate some curvature conditions admitting conformal $ \eta $-Ricci solitons on $ \epsilon $-Kenmotsu manifolds. Next, we consider gradient conformal $ \eta $-Ricci solitons and we present a characterization of the potential function. Finally, we develop an illustrative example for the existence of conformal $ \eta $-Ricci soliton on $ \epsilon $-Kenmotsu manifold.</p></abstract>

scholarly journals ∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds

2019 ◽  
Vol 69 (6) ◽  
pp. 1447-1458 ◽  
Author(s):  
Venkatesha ◽  
Devaraja Mallesha Naik ◽  
H. Aruna Kumara
Keyword(s):  
Vector Field ◽  
Ricci Soliton ◽  
Characteristic Vector ◽  
Ricci Solitons ◽  
Potential Vector ◽  
Open Set ◽  
Kenmotsu Manifolds ◽  
Almost Ricci Soliton ◽  
Characteristic Vector Field ◽  
Potential Vector Field

Abstract In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g 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 curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. 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.

scholarly journals D-Homothetically Deformed Kenmotsu Metric as a Ricci Soliton

2019 ◽  
Vol 33 (1) ◽  
pp. 143-152
Author(s):  
D.L. Kiran Kumar ◽  
H.G. Nagaraja ◽  
K. Venu
Keyword(s):  
Scalar Curvature ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Kenmotsu Manifolds

AbstractIn this paper we study the nature of Ricci solitons in D-homo-thetically deformed Kenmotsu manifolds. We prove that η -Einstein Kenmotsu metric as a Ricci soliton remains η -Einstein under D-homothetic deformation and the scalar curvature remains constant.

scholarly journals η-Ricci solitons in Kenmotsu manifolds

2019 ◽  
Vol 57 (2) ◽  
pp. 1-17
Author(s):  
Kanak Kanti Baishya ◽  
Partha Roy Chowdhury
Keyword(s):  
Ricci Soliton ◽  
Ricci Solitons ◽  
Kenmotsu Manifold ◽  
Metric Tensor ◽  
Kenmotsu Manifolds ◽  
Weakly Symmetric

Abstract The object of the present paper is to study generalized weakly symmetric and generalized weakly Ricci symmetric Kenmotsu manifolds whose metric tensor is η-Ricci soliton. The paper also aims to bring out curvature conditions for which η-Ricci solitons in Kenmotsu manifolds are sometimes shrinking or expanding and some other time remain steady. The existence of each generalized weakly symmetric and generalized weakly Ricci symmetric Kenmotsu manifold is ensured by an example.

scholarly journals ON THE MODIFIED FUTAKI INVARIANT OF COMPLETE INTERSECTIONS IN PROJECTIVE SPACES

2016 ◽  
Vol 222 (1) ◽  
pp. 186-209
Author(s):  
RYOSUKE TAKAHASHI
Keyword(s):  
Vector Field ◽  
Recent Work ◽  
Projective Spaces ◽  
Ricci Soliton ◽  
Complete Intersections ◽  
Necessary Condition ◽  
Ricci Solitons ◽  
Fano Varieties ◽  
Holomorphic Vector Field ◽  
Fano Manifold

Let $M$ be a Fano manifold. We call a Kähler metric ${\it\omega}\in c_{1}(M)$ a Kähler–Ricci soliton if it satisfies the equation $\text{Ric}({\it\omega})-{\it\omega}=L_{V}{\it\omega}$ for some holomorphic vector field $V$ on $M$. It is known that a necessary condition for the existence of Kähler–Ricci solitons is the vanishing of the modified Futaki invariant introduced by Tian and Zhu. In a recent work of Berman and Nyström, it was generalized for (possibly singular) Fano varieties, and the notion of algebrogeometric stability of the pair $(M,V)$ was introduced. In this paper, we propose a method of computing the modified Futaki invariant for Fano complete intersections in projective spaces.

scholarly journals Toric extremal Kähler-Ricci solitons are Kähler-Einstein

2017 ◽  
Vol 4 (1) ◽  
pp. 179-182 ◽  
Author(s):  
Simone Calamai ◽  
David Petrecca
Keyword(s):  
General Problem ◽  
Short Note ◽  
Kähler Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Toric Manifolds ◽  
Kahler Manifold

Abstract In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.

scholarly journals Kenmotsu manifolds admitting Schouten-Van Kampen Connection

2019 ◽  
pp. 23
Author(s):  
Nagaraja Gangadharappa Halammanavar ◽  
Kiran Kumar Lakshmana Devasandra
Keyword(s):  
Ricci Soliton ◽  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Equivalent Conditions

The objective of the present paper is to study Kenmotsu manifold admitting Schouten-van Kampen connection. We study Kenmotsu manifold admitting Schouten-van Kampen connection satisifying certain curvature conditions. Also we prove equivalent conditions for Ricci soliton in a Kenmotsu manifold is steady with respect to the Schouten-van Kampen connection.

Sign in / Sign up

Export Citation Format

Share Document