scholarly journals Some Symmetric Curvature Conditions on Kenmotsu Manifolds

2018 ◽  
Vol 1 (1) ◽  
pp. 50-56
Author(s):  
Riddhi Jung Shah
Keyword(s):  
Negative Curvature ◽  
Einstein Manifold ◽  
Constant Negative Curvature ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Kenmotsu Manifolds

In this paper, we study locally and globally φ-symmetric Kenmotsu manifolds. In both curvature conditions, it is proved that the manifold is of constant negative curvature - 1 and globally φ-Weyl projectively symmetric Kenmotsu manifold is an Einstein manifold. Finally, we give an example of 3-dimensional Kenmotsu manifold.

scholarly journals Some Symmetric Properties of Kenmotsu Manifolds Admitting Semi-Symmetric Metric Connection

2019 ◽  
pp. 35
Author(s):  
Venkatesha Venkatesh ◽  
Arasaiah Arasaiah ◽  
Vishnuvardhana Srivaishnava Vasudeva ◽  
Naveen Kumar Rahuthanahalli Thimmegowda
Keyword(s):  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Symmetric Properties

The object of the present paper is to study some symmetric propertiesof Kenmotsu manifold endowed with a semi-symmetric metric connection. Here weconsider pseudo-symmetric, Ricci pseudo-symmetric, projective pseudo-symmetric and -projective semi-symmetric Kenmotsu manifold with respect to semi-symmetric metric connection. Finally, we provide an example of 3-dimensional Kenmotsu manifold admitting a semi-symmetric metric connection which verify our results.

scholarly journals Geometry of Nonholonomic Kenmotsu Manifolds

2021 ◽  
pp. 84-87
Author(s):  
A.V. Bukusheva
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifold ◽  
Lie Derivative ◽  
Riemann Curvature Tensor ◽  
Intrinsic Geometry ◽  
Kenmotsu Manifold ◽  
Metric Tensor ◽  
Schouten Tensor ◽  
Kenmotsu Manifolds ◽  
Formal Properties

The concept of the intrinsic geometry of a nonholonomic Kenmotsu manifold M is introduced. It is understood as the set of those properties of the manifold that depend only on the framing  of the D^ distribution D of the manifold M, on the parallel transformation of vectors belonging to the distribution D along curves tangent to this distribution. The invariants of the intrinsic geometry of the nonholonomic Kenmotsu manifold are: the Schouten curvature tensor; 1-form η generating the distribution D; the Lie derivative  of the metric tensor g along the vector field ; Schouten — Wagner tensor field P, whose components in adapted coordinates are expressed using the equalities . It is proved that, as in the case of the Kenmotsu manifold, the Schouten — Wagner tensor of the manifold M vanishes. It follows that the Schouten tensor of a nonholonomic Kenmotsu manifold has the same formal properties as the Riemann curvature tensor. It is proved that the alternation of the Ricci — Schouten tensor coincides with the differential of the structural form. This property of the Ricci — Schouten tensor is used in the proof of the main result of the article: a nonholonomic Kenmotsu manifold cannot carry the structure of an η-Einstein manifold.

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.

scholarly journals On the Classification of Almost Kenmotsu Manifolds of Dimension 3

ISRN Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Classification Theorem ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Almost Kenmotsu Manifold ◽  
Geometric Conditions ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Weyl Manifold

This paper deals with the classification of a 3-dimensional almost Kenmotsu manifold satisfying certain geometric conditions. Moreover, by applying our main classification theorem, we obtain some suffcient conditions for an almost Kenmotsu manifold of dimension 3 to be an Einstein-Weyl manifold.

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 LEGENDRE CURVES ON 3-DIMENSIONAL f-KENMOTSU MANIFOLDS ADMITTING SCHOUTEN-VAN KAMPEN CONNECTION

2020 ◽  
pp. 357
Author(s):  
Ashis Mondal
Keyword(s):  
Three Dimensional ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Legendre Curve ◽  
Kenmotsu Manifolds ◽  
Legendre Curves ◽  
Slant Curves

In the present paper, biharmonic Legendre curves with respect to Schouten-Van Kampen connection have been studied on three-dimensional f-Kenmotsu manifolds. Locally $\phi $-symmetric Legendre curves on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen Connection have been introduced.Also slant curves have been studied on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen connection. Finally, we constract an example of a Legendre curve in a 3-dimensional f-Kenmotsu manifold.

scholarly journals Semi-Symmetric Metric Connection on Homothetic Kenmotsu Manifolds

2020 ◽  
Vol 12 (3) ◽  
pp. 223-232
Author(s):  
L. Thangmawia ◽  
R. Kumar
Keyword(s):  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Projectively Flat ◽  
Kenmotsu Manifolds ◽  
Metric Connection

The object of the paper is to study homothetic Kenmotsu manifold with respect to semi-symmetric metric connection. We discuss locally -symmetric homothetic Kenmotsu manifold and -projectively flat homothetic Kenmotsu manifold with respect to semi-symmetric metric connection. Finally, we construct an example of 3-dimensional homothetic Kenmotsu manifold to verify some results.

scholarly journals A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors

2016 ◽  
Vol 14 (1) ◽  
pp. 977-985 ◽  
Author(s):  
Yaning Wang
Keyword(s):  
Recent Result ◽  
Three Dimensional ◽  
Local Symmetry ◽  
Kenmotsu Manifold ◽  
Harmonic Curvature ◽  
Riemannian Product ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Curvature Tensors

AbstractLet M3 be a three-dimensional almost Kenmotsu manifold satisfying ▽ξh = 0. In this paper, we prove that the curvature tensor of M3 is harmonic if and only if M3 is locally isometric to either the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(−4) × ℝ. This generalizes a recent result obtained by [Wang Y., Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math., 2016, 116, 79-86] and [Cho J.T., Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J., 2016, 45, 435-442].

scholarly journals Legendre curves on 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3651-3656
Author(s):  
Wanxiao Tang ◽  
Pradip Majhi ◽  
Peibiao Zhao ◽  
Uday De
Keyword(s):  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Legendre Curve ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Legendre Curves ◽  
Slant Curves

The object of the present paper is to study biharmonic Legendre curves, locally ?-symmetric Legendre curves and slant curves in 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection. Finally, we construct an example of a Legendre curve in a 3-dimensional Kenmotsu manifold.

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