scholarly journals Kaehlerian manifolds with constant scalar curvature admitting a holomorphically projective vector field

1979 ◽  
Vol 14 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Kentaro Yano ◽  
Hitosi Hiramatu
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Projective Vector

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

2019 ◽  
Vol 16 (03) ◽  
pp. 1950039 ◽  
Author(s):  
V. Venkatesha ◽  
Devaraja Mallesha Naik
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Sasakian Manifold ◽  
Contact Metric Manifold ◽  
Reeb Vector Field ◽  
3 Dimensional ◽  
Flow Vector ◽  
Contact Metric Manifolds ◽  
Yamabe Soliton

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 3-DIMENSIONAL SASAKIAN METRIC AS A YAMABE SOLITON

2012 ◽  
Vol 09 (04) ◽  
pp. 1220003 ◽  
Author(s):  
RAMESH SHARMA
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Constant Curvature ◽  
Constant Scalar Curvature ◽  
Complete Manifold ◽  
3 Dimensional ◽  
Infinitesimal Automorphism ◽  
Contact Metric Structure ◽  
Sasakian Metric ◽  
Yamabe Soliton

If a 3-dimensional Sasakian metric on a complete manifold (M, g) is a Yamabe soliton, then we show that g has constant scalar curvature, and the flow vector field V is Killing. We further show that, either M has constant curvature 1, or V is an infinitesimal automorphism of the contact metric structure on M.

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

2020 ◽  
Vol 17 (12) ◽  
pp. 2050177
Author(s):  
Young Jin Suh ◽  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Three Dimensional ◽  
Constant Scalar Curvature ◽  
Infinitesimal Transformation ◽  
Contact Metric Manifold ◽  
Contact Manifolds ◽  
Flow Vector ◽  
Yamabe Solitons ◽  
Yamabe Soliton

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.

scholarly journals On warped product gradient η-Ricci solitons

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5791-5801 ◽  
Author(s):  
Adara Blaga
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Warped Product ◽  
Constant Scalar Curvature ◽  
Ricci Soliton ◽  
Product Manifold ◽  
Potential Vector ◽  
Warped Product Manifold ◽  
Gradient Type ◽  
Potential Vector Field

If the potential vector field of an ?-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a nonlinear second order PDE. In a particular case of irrotational potential vector field we prove that the soliton is completely determined by f . We give a way to construct a gradient ?-Ricci soliton on a warped product manifold and show that if the base manifold is oriented, compact and of constant scalar curvature, the soliton on the product manifold gives a lower bound for its scalar curvature.

scholarly journals Some results on Ricci-Bourguignon solitons and almost solitons

2020 ◽  
pp. 1-14
Author(s):  
Shubham Dwivedi
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Integral Formula ◽  
Constant Scalar Curvature ◽  
Ricci Solitons ◽  
Euclidean Sphere ◽  
Integral Formulas

Abstract We prove some results for the solitons of the Ricci–Bourguignon flow, generalizing the corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci–Bourguignon almost solitons and prove some results about them that generalize previous results for Ricci almost solitons. We also derive integral formulas for compact gradient Ricci–Bourguignon solitons and compact gradient Ricci–Bourguignon almost solitons. Finally, using the integral formula, we show that a compact gradient Ricci–Bourguignon almost soliton is isometric to a Euclidean sphere if it has constant scalar curvature or its associated vector field is conformal.

Randers Metrics of Constant Scalar Curvature

2013 ◽  
Vol 56 (3) ◽  
pp. 615-620
Author(s):  
Sevim Esra Sengelen ◽  
Zhongmin Shen
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Special Class ◽  
Constant Scalar Curvature ◽  
Riemannian Metric ◽  
Finsler Metrics ◽  
Randers Metric ◽  
Randers Metrics

Abstract.Randers metrics are a special class of Finsler metrics. Every Randers metric can be expressed in terms of a Riemannian metric and a vector field via Zermelo navigation. In this paper, we show that a Randers metric has constant scalar curvature if the Riemannian metric has constant scalar curvature and the vector field is homothetic

scholarly journals ON RICCI-BOURGUIGNON h-ALMOST SOLITONS IN RIEMANNIAN MANIFOLDS

2020 ◽  
Vol 20 (3) ◽  
pp. 673-680
Author(s):  
YASEMIN SOYLU
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Integral Formula ◽  
Constant Scalar Curvature ◽  
Ricci Soliton ◽  
Almost Ricci Soliton ◽  
Structure Equations ◽  
Isometric To A Sphere

In this paper, we shall give some structure equations for RB h-almost solitons which generalize previous results for Ricci almost solitons. As a consequence of these equations we also derive an integral formula for the compact gradient RB h-almost solitons which enables us to show that a compact nontrivial almost Ricci soliton is isometric to a sphere provided either it has constant scalar curvature or its associated vector field is conformal.

Generalized -Einstein Real Hypersurfaces in and

2020 ◽  
Vol 63 (4) ◽  
pp. 909-920
Author(s):  
Yaning Wang
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Constant Coefficient ◽  
Real Hypersurface ◽  
Constant Mean Curvature ◽  
Constant Scalar Curvature ◽  
Real Hypersurfaces

AbstractIn this paper we obtain some new characterizations of pseudo-Einstein real hypersurfaces in $\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$. More precisely, we prove that a real hypersurface in $\mathbb{C}P^{2}$ or $\mathbb{C}H^{2}$ with constant mean curvature is generalized ${\mathcal{D}}$-Einstein with constant coefficient if and only if it is pseudo-Einstein. We prove that a real hypersurface in $\mathbb{C}P^{2}$ with constant scalar curvature is generalized ${\mathcal{D}}$-Einstein with constant coefficient if and only if it is pseudo-Einstein.

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