Ricci Solitons in Kenmotsu Manifold under Generalized D-Conformal Deformation

2019 ◽  
Vol 40 (2) ◽  
pp. 195-200
Author(s):  
H. G. Nagaraja ◽  
D. L. Kiran Kumar
Keyword(s):  
Ricci Solitons ◽  
Conformal Deformation ◽  
Kenmotsu Manifold

Some Ricci solitons on Kenmotsu manifold

2020 ◽  
Vol 28 (4) ◽  
pp. 1155-1164
Author(s):  
B. Shanmukha ◽  
V. Venkatesha
Keyword(s):  
Ricci Solitons ◽  
Kenmotsu Manifold

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 in three-dimensional trans-Sasakian manifolds

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 363-370 ◽  
Author(s):  
Mine Turan ◽  
Chand De ◽  
Ahmet Yildiz
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Sasakian Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Sasakian Manifolds ◽  
Kenmotsu Manifold ◽  
Constant Multiple ◽  
3 Dimensional ◽  
Gradient Ricci Solitons

The object of the present paper is to study 3-dimensional trans-Sasakian manifolds admitting Ricci solitons and gradient Ricci solitons. We prove that if (1,V, ?) is a Ricci soliton where V is collinear with the characteristic vector field ?, then V is a constant multiple of ? and the manifold is of constant scalar curvature provided ?, ? =constant. Next we prove that in a 3-dimensional trans-Sasakian manifold with constant scalar curvature if 1 is a gradient Ricci soliton, then the manifold is either a ?-Kenmotsu manifold or an Einstein manifold. As a consequence of this result we obtain several corollaries.

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 Ricci solitons in a generalized weakly (Ricci) symmetric D-homothetically deformed Kenmotsu manifold

2019 ◽  
Vol 18 (1) ◽  
pp. 123-136
Author(s):  
Adara M. Blaga ◽  
Kanak Kanti Baishya ◽  
Nihar Sarkar
Keyword(s):  
Ricci Solitons ◽  
Kenmotsu Manifold ◽  
Weakly Symmetric

Abstract The object of the present paper is to investigate the nature of Ricci solitons on D-homothetically deformed Kenmotsu manifold with generalized weakly symmetric and generalized weakly Ricci symmetric curvature restrictions.

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 *-conformal η-Ricci solitons in ϵ-Kenmotsu manifolds

2020 ◽  
Vol 108 (122) ◽  
pp. 91-102
Author(s):  
Abdul Haseeb ◽  
Rajendra Prasad
Keyword(s):  
Ricci Solitons ◽  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds

We characterize ?-Kenmotsu manifolds admitting *-conformal ?- Ricci solitons. At last, an example of 7-dimension ?-Kenmotsu manifold is given.

scholarly journals *-Ricci Solitons on Kenmotsu Manifold

2018 ◽  
Vol 30 (11) ◽  
pp. 401-408
Author(s):  
SUSHIL SHUKLA ◽  
◽  
SHIKHA TIWARI ◽  
Keyword(s):  
Ricci Solitons ◽  
Kenmotsu Manifold

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 ETA-RICCI SOLITONS ON KENMOTSU MANIFOLD WITH GENERALIZED SYMMETRIC METRIC CONNECTION

2020 ◽  
pp. 295
Author(s):  
Mohd Danish Siddiqi ◽  
Oğuzhan Bahadır
Keyword(s):  
Ricci Solitons ◽  
Kenmotsu Manifold ◽  
Metric Connection ◽  
Alpha Beta

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 symmetric metric connection of type $(\alpha,\beta)$ satisfying the conditions $\bar{R}.\bar{S}=0$, $\bar{S}.\bar{R}=0$, $\bar{W_{2}}.\bar{S}=0$ and $\bar{S}.\bar{W_{2}}=0.$. Finally, we construct an example of Kenmotsu manifold with generalized symmetric metric connection of type $(\alpha,\beta)$ admitting $\eta$-Ricci solitons.

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