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 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 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 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 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.

scholarly journals *-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds

2019 ◽  
Vol 17 (1) ◽  
pp. 874-882 ◽  
Author(s):  
Xinxin Dai ◽  
Yan Zhao ◽  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Ricci Soliton ◽  
Contact Transformation ◽  
Kenmotsu Manifold ◽  
Potential Vector ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Dimension 2 ◽  
Potential Vector Field

Abstract Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.

scholarly journals η-Ricci Solitons on Sasakian 3-Manifolds

2017 ◽  
Vol 55 (2) ◽  
pp. 143-156
Author(s):  
Pradip Majhi ◽  
Uday Chand De ◽  
Debabrata Kar
Keyword(s):  
Ricci Tensor ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Conformally Flat ◽  
Curvature Condition ◽  
Cyclic Parallel Ricci Tensor ◽  
Codazzi Type ◽  
Parallel Ricci Tensor

AbstractIn this paper we studyη-Ricci solitons on Sasakian 3-manifolds. Among others we prove that anη-Ricci soliton on a Sasakian 3-manifold is anη-Einstien manifold. Moreover we considerη-Ricci solitons on Sasakian 3-manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Beside these we study conformally flat andφ-Ricci symmetricη-Ricci soliton on Sasakian 3-manifolds. Alsoη-Ricci soliton on Sasakian 3-manifolds with the curvature conditionQ.R= 0 have been considered. Finally, we construct an example to prove the non-existence of properη-Ricci solitons on Sasakian 3-manifolds and verify some results.

scholarly journals Some characterizations of three-dimensional trans-Sasakian manifolds admitting η- Ricci solitons and trans-Sasakian manifolds as Kagan subprojective space

2020 ◽  
Vol 72 (3) ◽  
pp. 427-432
Author(s):  
A. Sarkar ◽  
A. Sil ◽  
A. K. Paul
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Second Order ◽  
Ricci Solitons ◽  
Riemann Curvature ◽  
Sasakian Manifolds ◽  
Riemann Curvature Tensor ◽  
Order Parallel

UDC 514.7 The object of the present paper is to study three-dimensional trans-Sasakian manifolds admitting η -Ricci soliton. Actually, we study such manifolds whose Ricci tensor satisfy some special conditions like cyclic parallelity, Ricci semisymmetry, ϕ -Ricci semisymmetry, after reviewing the properties of second order parallel tensors on such manifolds. We determine the form of Riemann curvature tensor of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces. We also give some classification results of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces.

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 Gradient Ricci solitons on almost Kenmotsu manifolds

2015 ◽  
Vol 98 (112) ◽  
pp. 227-235 ◽  
Author(s):  
Yaning Wang ◽  
Uday De ◽  
Ximin Liu
Keyword(s):  
Ricci Soliton ◽  
Einstein Metric ◽  
Dimensional Manifold ◽  
Kenmotsu Manifold ◽  
Riemannian Product ◽  
Gradient Ricci Soliton ◽  
Almost Kenmotsu Manifold ◽  
Gradient Ricci Solitons ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds

If the metric of an almost Kenmotsu manifold with conformal Reeb foliation is a gradient Ricci soliton, then it is an Einstein metric and the Ricci soliton is expanding. Moreover, let (M2n+1,?,?,?,g) be an almost Kenmotsu manifold with ? belonging to the (k,?)?-nullity distribution and h h?0. If the metric g of M2n+1 is a gradient Ricci soliton, then M2n+1 is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a at n-dimensional manifold, also, the Ricci soliton is expanding with ? = 4n.

scholarly journals On para-Kenmotsu manifolds

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4971-4980 ◽  
Author(s):  
Simeon Zamkovoy
Keyword(s):  
Sectional Curvature ◽  
Ricci Tensor ◽  
Constant Scalar Curvature ◽  
Holomorphic Sectional Curvature ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Locally Conformally Flat ◽  
Parallel Ricci Tensor ◽  
Negative Sectional Curvature

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 ?-Einstein manifolds. We show that a locally conformally flat para-Kenmotsu manifold is a space of constant negative sectional curvature -1 and we prove that if a para-Kenmotsu manifold is a space of constant ?-para-holomorphic sectional curvature H, then it is a space of constant sectional curvature and H = -1. Finally the object of the present paper is to study a 3-dimensional para-Kenmotsu manifold, satisfying certain curvature conditions. Among other, it is proved that any 3-dimensional para-Kenmotsu manifold with ?-parallel Ricci tensor is of constant scalar curvature and any 3-dimensional para-Kenmotsu manifold satisfying cyclic Ricci tensor is a manifold of constant negative sectional curvature -1.

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