On Kenmotsu manifolds admitting η-Ricci-Yamabe solitons

Kenmotsu Manifold ◽

Kenmotsu Manifolds ◽

Yamabe Solitons ◽

The objective of this paper is to deal with Kenmotsu manifolds admitting [Formula: see text]-Ricci-Yamabe solitons. First, it is proved that if a Kenmotsu manifold [Formula: see text] which admits an [Formula: see text]-Ricci-Yamabe soliton, then the manifold [Formula: see text] is Einstein and is of constant scalar curvature. Then, some important characterizations, which classify Kenmotsu manifolds admitting such solitons, are obtained and an example given which supports our results.

Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold

Mathematica Slovaca ◽

10.1515/ms-2017-0340 ◽

2020 ◽

Vol 70 (1) ◽

pp. 151-160

Author(s):

Amalendu Ghosh

Keyword(s):

Scalar Curvature ◽

Warped Product ◽

Product Structure ◽

Kenmotsu Manifold ◽

Kenmotsu Manifolds ◽

Almost Kenmotsu Manifolds ◽

AbstractIn this paper, we study Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold. First, we prove that if a Kenmotsu metric is a Yamabe soliton, then it has constant scalar curvature. Examples has been provided on a larger class of almost Kenmotsu manifolds, known as β-Kenmotsu manifold. Next, we study quasi Yamabe soliton on a complete Kenmotsu manifold M and proved that it has warped product structure with constant scalar curvature in a region Σ where ∣Df∣ ≠ 0.

Conformal Geometry Solitons

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.472-475.123 ◽

2012 ◽

Vol 472-475 ◽

pp. 123-126

Author(s):

Rong Rong Cao ◽

Xiang Gao

Keyword(s):

Scalar Curvature ◽

Compact Manifold ◽

Hilbert Function ◽

Conformal Geometry ◽

Yamabe Flow ◽

Noncompact Manifolds ◽

Monotone Formula ◽

Yamabe Solitons ◽

In this paper, we deal with a generalization of the Yamabe flow named conformal geometry flow. Firstly we derive a monotone formula of the Einstein-Hilbert functional under the conformal geometry flow. Then we prove the properties that the conformal geometry solitons and conformal geometry breather both have constant scalar curvature at each time by using the modified Einstein-Hilbert function. Finally we present some properties of Yamabe solitons in compact manifold and noncompact manifolds through the equation of Yamabe soliton.

Yamabe solitons and gradient Yamabe solitons on three-dimensional N(k)-contact manifolds

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887820501777 ◽

2020 ◽

Vol 17 (12) ◽

pp. 2050177

Author(s):

Young Jin Suh ◽

Uday Chand De

Keyword(s):

Vector Field ◽

Scalar Curvature ◽

Three Dimensional ◽

Infinitesimal Transformation ◽

Contact Metric Manifold ◽

Contact Manifolds ◽

Flow Vector ◽

Yamabe Solitons ◽

If a three-dimensional [Formula: see text]-contact metric manifold [Formula: see text] admits a Yamabe soliton of type [Formula: see text], then the manifold has a constant scalar curvature and the flow vector field [Formula: see text] is Killing. Furthermore, either [Formula: see text] has a constant curvature [Formula: see text] or the flow vector field [Formula: see text] is a strict contact infinitesimal transformation. Also, we prove that if the metric of a three-dimensional [Formula: see text]-contact metric manifold [Formula: see text] admits a gradient Yamabe soliton, then either the manifold is flat or the scalar curvature is constant. Moreover, either the potential function is constant or the manifold is of constant sectional curvature [Formula: see text]. Finally, we have given an example to verify our result.

Yamabe solitons on 3-dimensional contact metric manifolds with Qφ = φQ

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819500397 ◽

2019 ◽

Vol 16 (03) ◽

pp. 1950039 ◽

Cited By ~ 8

Author(s):

V. Venkatesha ◽

Devaraja Mallesha Naik

Keyword(s):

Vector Field ◽

Scalar Curvature ◽

Sasakian Manifold ◽

Contact Metric Manifold ◽

Reeb Vector Field ◽

3 Dimensional ◽

Flow Vector ◽

Contact Metric Manifolds ◽

If [Formula: see text] is a 3-dimensional contact metric manifold such that [Formula: see text] which admits a Yamabe soliton [Formula: see text] with the flow vector field [Formula: see text] pointwise collinear with the Reeb vector field [Formula: see text], then we show that the scalar curvature is constant and the manifold is Sasakian. Moreover, we prove that if [Formula: see text] is endowed with a Yamabe soliton [Formula: see text], then either [Formula: see text] is flat or it has constant scalar curvature and the flow vector field [Formula: see text] is Killing. Furthermore, we show that if [Formula: see text] is non-flat, then either [Formula: see text] is a Sasakian manifold of constant curvature [Formula: see text] or [Formula: see text] is an infinitesimal automorphism of the contact metric structure on [Formula: see text].

A note on warped product almost quasi-Yamabe solitons

Filomat ◽

10.2298/fil1907009b ◽

2019 ◽

Vol 33 (7) ◽

pp. 2009-2016 ◽

Cited By ~ 5

Author(s):

Adara Blaga

Keyword(s):

Riemannian Manifolds ◽

Warped Product ◽

Sufficient Conditions ◽

Product Manifold ◽

Base Manifold ◽

Warped Product Manifold ◽

Necessary And Sufficient ◽

Yamabe Solitons ◽

We consider almost quasi-Yamabe solitons in Riemannian manifolds, derive a Bochner-type formula in the gradient case and prove that under certain assumptions, the manifold is of constant scalar curvature. We also provide necessary and sufficient conditions for a gradient almost quasi-Yamabe soliton on the base manifold to induce a gradient almost quasi-Yamabe soliton on the warped product manifold.

On para-Kenmotsu manifolds

Filomat ◽

10.2298/fil1814971z ◽

2018 ◽

Vol 32 (14) ◽

pp. 4971-4980 ◽

Cited By ~ 2

Author(s):

Simeon Zamkovoy

Keyword(s):

Sectional Curvature ◽

Ricci Tensor ◽

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.

Conformal vector fields and Yamabe solitons

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819500531 ◽

2019 ◽

Vol 16 (04) ◽

pp. 1950053

Author(s):

Nasser Bin Turki ◽

Bang-Yen Chen ◽

Sharief Deshmukh

Keyword(s):

Scalar Curvature ◽

Vector Fields ◽

Sufficient Conditions ◽

Conformal Vector ◽

Conformal Vector Fields ◽

Yamabe Solitons

In this paper, we use less topological restrictions and more geometric and analytic conditions to obtain some sufficient conditions on Yamabe solitons such that their metrics are Yamabe metrics, that is, metrics of constant scalar curvature. More precisely, we use properties of conformal vector fields to find several sufficient conditions on the soliton vector fields of Yamabe solitons under which their metrics are Yamabe metrics.

On complete Yamabe solitons

Advances in Geometry ◽

10.1515/advgeom-2017-0018 ◽

2018 ◽

Vol 18 (1) ◽

pp. 101-104 ◽

Cited By ~ 4

Author(s):

B. Bidabad ◽

M. Yar Ahmadi

Keyword(s):

Fundamental Group ◽

Scalar Curvature ◽

Sphere Bundle ◽

Finite Fundamental Group ◽

Yamabe Solitons ◽

AbstractIn this paper we study an extension of Yamabe solitons for inequalities. We show that a Riemannian complete non-compact shrinking Yamabe soliton (M,g,V,λ) has finite fundamental group, provided that the scalar curvature is strictly bounded above byλ. Furthermore, an instance of illustrating the sharpness of this inequality is given. We also mention that the fundamental group of the sphere bundleSMis finite.

Ricci solitons and gradient Ricci solitons in three-dimensional trans-Sasakian manifolds

Filomat ◽

10.2298/fil1202363t ◽

2012 ◽

Vol 26 (2) ◽

pp. 363-370 ◽

Cited By ~ 6

Author(s):

Mine Turan ◽

Chand De ◽

Ahmet Yildiz

Keyword(s):

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.

SOME RESULTS ON (ϵ)- KENMOTSU MANIFOLDS

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2001273s ◽

2020 ◽

Vol 35 (1) ◽

pp. 273

Author(s):

Arpan Sardar

Keyword(s):

Scalar Curvature ◽

Kenmotsu Manifold ◽

Kenmotsu Manifolds

We have studied curvature symmetries in ($\epsilon$)-Kenmotsu manifolds. Next, we have proved the non-existence of a non-zero parallel 2-form in an ($\epsilon$)-Kenmotsu manifold. Moreover, we have characterised $\phi$-Ricci symmetric ($\epsilon$)-Kenmotsu manifolds and finally, we have proved that under certain restriction on the scalar curvature $divR$=0 and $divC$=0 are equivalent, where `$div$' denotes divergence.