scholarly journals Concircular curvature tensor of Kenmotsu manifolds admitting generalized Tanaka-Webster connection

2019 ◽  
Keyword(s):  
Curvature Tensor ◽  
Kenmotsu Manifolds ◽  
Concircular Curvature Tensor

scholarly journals On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions

2018 ◽  
Vol 33 (2) ◽  
pp. 255
Author(s):  
Dibakar Dey ◽  
Pradip Majhi
Keyword(s):  
Vector Field ◽  
Curvature Tensor ◽  
Conformally Flat ◽  
Kenmotsu Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

The object of the present paper is to characterize quasi-conformally flat and $\xi$-quasi-conformally flat almost Kenmotsu manifolds with  $(k,\mu)$-nullity and $(k,\mu)'$-nullity distributions respectively. Also we characterize almost Kenmotsu manifolds with vanishing extended quasi-conformal curvature tensor and extended $\xi$-quasi-conformally flat almost Kenmotsu manifolds such that the characteristic vector field $\xi$ belongs to the $(k,\mu)$-nullity distribution.

On geometry of Kenmotsu manifolds with N-connection

2019 ◽  
pp. 48-60
Author(s):  
A. Bukusheva
Keyword(s):  
Vector Field ◽  
Coordinate System ◽  
Curvature Tensor ◽  
Tensor Field ◽  
Lie Derivative ◽  
Kenmotsu Manifold ◽  
Metric Tensor ◽  
Civita Connection ◽  
Kenmotsu Manifolds ◽  
Levi Civita Connection

A Kenmotsu manifold with a given N-connection is considered. From the integrability of the distribution of a Kenmotsu manifold it follows that the N-connection belongs to the class of the quarter-symmetric connections. Among the N-connections, the class of connections adapted to the structure of the Kenmotsu manifold is specified. In particular, it is proved that an N-connection preserves the structure endomorphism φ of the Kenmotsu manifold if and only if the endomorphisms N and φ commute. A formula expressing the N-connection in terms of the Levi-Civita connection is obtained. The Chrystoffel symbols of the Levi-Civita connection and of the N-connection of the Kenmotsu manifold with respect to the adapted coordinates are computed. The properties of the invariants of the interior geometry of the Kenmotsu manifolds are investigated. The invariants of the interior geometry are the following: the Schouten curvature tensor; the 1-form  defining the distribution D; the Lie derivative 0   L g of the metric tensor g along the vector field ;  the tensor field P with the components given with respect to the adapted coordinate system by the formula Pacd  ncad . The field P is called in the work the Schouten — Wagner tensor. It is proved that the Schouten — Wagner tensor of the interior connection of the Kenmotsu manifold is zero. The conditions that satisfies the endomorphism N defining the metric N-connection are found. At the end of the work, an example of a Kenmotsu manifold with a metric N-connection preserving the structure endomorphism φ is given.

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 A Study on Conservative C-Bochner Curvature Tensor in K-Contact and Kenmotsu Manifolds Admitting Semisymmetric Metric Connection

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Gurupadavva Ingalahalli ◽  
C. S. Bagewadi
Keyword(s):  
Curvature Tensor ◽  
Civita Connection ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Levi Civita Connection

The paper deals with the study on conservative C-Bochner curvature tensor in K-contact and Kenmotsu manifolds admitting semisymmetric metric connection, and it is shown that these manifolds are η-Einstein with respect to Levi-Civita connection, and the results are illustrated with examples.

scholarly journals On almost Kenmotsu manifolds with nullity distributions

2017 ◽  
Vol 48 (3) ◽  
pp. 251-262 ◽  
Author(s):  
Uday Chand De ◽  
Jae Bok Jun ◽  
Krishanu Mandal
Keyword(s):  
Vector Field ◽  
Curvature Tensor ◽  
Characteristic Vector ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Projective Curvature ◽  
Nullity Distribution ◽  
Projective Curvature Tensor ◽  
Characteristic Vector Field

The object of this paper is to characterize the curvature conditions $R\cdot P=0$ and $P\cdot S=0$ with its characteristic vector field $\xi$ belonging to the $(k,\mu)'$-nullity distribution and $(k,\mu)$-nullity distribution respectively, where $P$ is the Weyl projective curvature tensor. As a consequence of the main results we obtain several corollaries.

scholarly journals Geometry of concircular curvature tensor of Kahler manifolds

2020 ◽  
Vol 25 (2) ◽  
pp. 110
Author(s):  
Rawah A. Zaben1 ◽  
, Rana H. Jasim2
Keyword(s):  
Curvature Tensor ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Necessary Condition ◽  
Kahler Manifolds ◽  
Geometrical Meaning ◽  
Nearly Kähler ◽  
Concircular Curvature Tensor ◽  
Nearly Kähler Manifold ◽  
The Relationship

The study deals with the necessary condition where a nearly Kahler manifold of flat concircular tensor has been found. And the relationship between these invariants and additional properties of symmetry concircular tensor, as well as geometrical meaning of the reference in zero of these invariants .   http://dx.doi.org/10.25130/tjps.25.2020.037

scholarly journals Spacetimes Admitting Concircular Curvaure Tensor in f(R) Gravity

2022 ◽  
Vol 9 ◽  
Author(s):  
Uday Chand De ◽  
Sameh Shenawy ◽  
H. M. Abu-Donia ◽  
Nasser Bin Turki ◽  
Suliman Alsaeed ◽  
...  
Keyword(s):  
Energy Density ◽  
Perfect Fluid ◽  
Curvature Tensor ◽  
Ricci Tensor ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Isotropic Pressure ◽  
Concircular Curvature Tensor ◽  
Fluid Spacetimes

The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.

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