An Einstein-like metric on almost Кenmotsu manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4695-4702 ◽  
Author(s):  
Yaning Wang ◽  
Wenjie Wang
Keyword(s):  
Scalar Curvature ◽  
Hyperbolic Space ◽  
Critical Condition ◽  
Three Dimensional ◽  
Constant Scalar Curvature ◽  
Kenmotsu Manifold ◽  
Almost Kenmotsu Manifold

In this paper, we prove that if the metric of a three-dimensional (k,?)'-almost Kenmotsu manifold satisfies the Miao-Tam critical condition, then the manifold is locally isometric to the hyperbolic space H3(-1). Moreover, we prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation satisfies the Miao-Tam critical condition, then the manifold is either of constant scalar curvature or Einstein. Some corollaries of main results are also given.

scholarly journals Ricci recurrent almost Kenmotsu 3-manifolds

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2293-2301
Author(s):  
V. Venkatesha ◽  
Aruna Kumara ◽  
Devaraja Naik
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Kenmotsu Manifold ◽  
Riemannian Product ◽  
3 Dimensional ◽  
Almost Kenmotsu Manifold

In this paper, we obtain that a Ricci recurrent 3-dimensional almost Kenmotsu manifold with constant scalar curvature satisfying ??h = 0,h ? 0, is locally isometric to the Riemannian product H2(-4)xR.

A Note on Randers Metrics of Scalar Flag Curvature

2012 ◽  
Vol 55 (3) ◽  
pp. 474-486 ◽  
Author(s):  
Bin Chen ◽  
Lili Zhao
Keyword(s):  
Scalar Curvature ◽  
Three Dimensional ◽  
Constant Scalar Curvature ◽  
Flag Curvature ◽  
Projectively Flat ◽  
Randers Metrics

AbstractSome families of Randers metrics of scalar flag curvature are studied in this paper. Explicit examples that are neither locally projectively flat nor of isotropic S-curvature are given. Certain Randers metrics with Einstein α are considered and proved to be complex. Three dimensional Randers manifolds, with α having constant scalar curvature, are studied.

Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold

2020 ◽  
Vol 70 (1) ◽  
pp. 151-160
Author(s):  
Amalendu Ghosh
Keyword(s):  
Scalar Curvature ◽  
Warped Product ◽  
Constant Scalar Curvature ◽  
Product Structure ◽  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Yamabe Soliton

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.

Hyperbolic submanifolds with finite type hyperbolic Gauss map

2015 ◽  
Vol 26 (02) ◽  
pp. 1550014 ◽  
Author(s):  
Uğur Dursun ◽  
Rüya Yeğin
Keyword(s):  
Scalar Curvature ◽  
Finite Type ◽  
Hyperbolic Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Scalar Curvature ◽  
Gauss Map ◽  
Hyperbolic Spaces ◽  
Nonzero Constant ◽  
Hyperbolic Gauss Map

We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface Mn with nonzero constant mean curvature in a hyperbolic space [Formula: see text] has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space [Formula: see text] having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in [Formula: see text] has biharmonic hyperbolic Gauss map.

Hypersurfaces of the hyperbolic space with constant scalar curvature

2005 ◽  
Vol 48 (1-2) ◽  
pp. 65-88 ◽  
Author(s):  
Zejun Hu ◽  
Shujie Zhai
Keyword(s):  
Scalar Curvature ◽  
Hyperbolic Space ◽  
Constant Scalar Curvature

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.

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.

CONFORMAL TRANSFORMATIONS OF COMPACT SELF-DUAL MANIFOLDS

1994 ◽  
Vol 05 (01) ◽  
pp. 125-140 ◽  
Author(s):  
Y. S. POON
Keyword(s):  
Scalar Curvature ◽  
Symmetry Group ◽  
Positive Constant ◽  
Three Dimensional ◽  
Constant Scalar Curvature ◽  
Topological Classification ◽  
Conformal Transformations ◽  
Conformal Class ◽  
Zero Scalar Curvature

We prove that when the dimension of the group of conformal transformations of a compact self-dual manifold is at least three, the conformal class contains either a metric with positive constant scalar curvature or a metric with zero scalar curvature. This result is combined with a topological classification of 4-manifolds to provide a complete geometrical classification of the compact self-dual manifolds whose symmetry group is at least three-dimensional.

scholarly journals Curvature properties of almost Kenmotsu manifolds with generalized nullity conditions

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3807-3816
Author(s):  
Yaning Wang ◽  
Wenjie Wang
Keyword(s):  
Hyperbolic Space ◽  
Local Symmetry ◽  
Kenmotsu Manifold ◽  
Riemannian Product ◽  
Almost Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Weak Symmetry

In this paper, it is proved that on a generalized (k,?)'-almost Kenmotsu manifold M2n+1 of dimension 2n + 1, n > 1, the conditions of local symmetry, semi-symmetry, pseudo-symmetry and quasi weak-symmetry are equivalent and this is also equivalent to that M2n+1 is locally isometric to either the hyperbolic space H2n+1(-1) or the Riemannian product Hn+1(-4)xRn. Moreover, we also prove that a generalized (k,?)-almost Kenmotsu manifold of dimension 2n + 1, n > 1, is pseudo-symmetric if and only if it is locally isometric to the hyperbolic space H2n+1(-1).

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