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.

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 The curvature and topological properties of hypersurfaces with constant scalar curvature

2004 ◽  
Vol 70 (1) ◽  
pp. 35-44
Author(s):  
Shu Shichang ◽  
Liu Sanyang
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Constant Scalar Curvature ◽  
Second Fundamental Form ◽  
Topological Properties ◽  
Spherical Space ◽  
Riemannian Product ◽  
3 Dimensional ◽  
The Second Fundamental Form ◽  
Spherical Space Form

In this paper, we consider n (n ≥ 3)-dimensional compact oriented connected hypersurfaces with constant scalar curvature n(n − 1)r in the unit sphere Sn+1(1). We prove that, if r ≥ (n − 2)/(n − 1) and S ≤ (n − 1)(n(r − 1) + 2)/(n − 2) + (n − 2)/(n(r − 1) + 2), then either M is diffeomorphic to a spherical space form if n = 3; or M is homeomorphic to a sphere if n ≥ 4; or M is isometric to the Riemannian product , where c2 = (n − 2)/(nr) and S is the squared norm of the second fundamental form of M.

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.

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].

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.

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 Second order parallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 839-847 ◽  
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Second Order ◽  
Dimensional Manifold ◽  
Kenmotsu Manifold ◽  
Metric Tensor ◽  
Riemannian Product ◽  
Almost Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Order Parallel

In this paper, we prove that if there exists a second order symmetric parallel tensor on an almost Kenmotsu manifold (M2n+1, ?, ?, ?, g) whose characteristic vector field ? belongs to the (k,?)'-nullity distribution, then either M2n+1 is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, or the second order parallel tensor is a constant multiple of the associated metric tensor of M2n+1. Furthermore, some properties of an almost Kenmotsu manifold admitting a second order parallel tensor with ? belonging to the (k,?)-nullity distribution are also obtained.

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.

COMPACT LOCALLY CONFORMALLY FLAT RIEMANNIAN MANIFOLDS

2001 ◽  
Vol 33 (4) ◽  
pp. 459-465 ◽  
Author(s):  
QING-MING CHENG
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Space Form ◽  
Constant Scalar Curvature ◽  
Topological Classification ◽  
Conformally Flat ◽  
Riemannian Product ◽  
Locally Conformally Flat

First, we shall prove that a compact connected oriented locally conformally flat n-dimensional Riemannian manifold with constant scalar curvature is isometric to a space form or a Riemannian product Sn−1(c) × S1 if its Ricci curvature is nonnegative. Second, we shall give a topological classification of compact connected oriented locally conformally flat n-dimensional Riemannian manifolds with nonnegative scalar curvature r if the following inequality is satisfied: [sum ]i,jR2ij [les ] r2/(n−1), where [sum ]i,jR2ij is the squared norm of the Ricci curvature tensor.

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