scholarly journals On Almost α‐Kenmotsu Manifolds with Some Tensor Fields

2016 ◽  
Vol 16 (2) ◽  
pp. 256-264
Author(s):  
Hakan Öztürk
Keyword(s):  
Tensor Fields ◽  
Kenmotsu Manifolds

scholarly journals Characterization theorems on warped product semi-slant submanifolds in Kenmotsu manifolds

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4033-4043 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Ali Alkhaldi
Keyword(s):  
Warped Product ◽  
Tensor Fields ◽  
Slant Submanifold ◽  
Kenmotsu Manifold ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds ◽  
Characterization Theorems

In this paper, we deal with the study of warped product semi-slant submanifolds isometrically immersed into a Kenmotsu manifold. We prove two characterization theorems for a warped product semi-slant submanifold in Kenmotsu manifolds in terms of the tensor fields.

Kenmotsu Manifolds with Zero Ricci-Schouten Tensor

2020 ◽  
pp. 10-16
Author(s):  
Aliya V. Bukusheva
Keyword(s):  
Vector Field ◽  
Vector Bundle ◽  
Einstein Manifold ◽  
Parallel Transport ◽  
Lie Derivative ◽  
Tensor Fields ◽  
Kenmotsu Manifold ◽  
Metric Tensor ◽  
Schouten Tensor ◽  
Kenmotsu Manifolds

The paper is dedicated to the investigation of the interior geometry of the Kenmotsu manifolds M. By the interior geometry of the manifold M we mean the aggregate of the properties of the manifold that depend only on the closing of the distribution D of the Kenmotsu manifold as well as on the parallel transport of the vectors from the distribution D along arbitrary curves of the manifold. The invariants of the interior geometry of a Kenmotsu manifold are the following: the Schouten curvature tensor; the 1-form η generating the distribution D; the Lie derivative of the metric tensor g along the structure vector field ; the Schouten-Wagner admissible tensor fields with the components with respect to adapted coordinates; the structural endomorphism φ; the endomorphism N that allows to prolong the interior connection to a connection in a vector bundle. A special attention is payed to the Ricci-Schouten tensor. In particular, it is stated that a Kenmotsu manifold with zero Ricci-Schouten tensor is an Einstein manifold. Conversely, if M is an η-Einstein Kenmotsu manifold and then M is an Einstein manifold with zero Ricci-Schouten tensor. It is proved that the Ricci-Schouten tensor is zero if and only if the Kenmotsu manifold M is locally Ricci-symmetric. This implies the following well-known result: a Kenmotsu manifold is an Einstein manifold if and only if it is locally Ricci-symmetric. An N-connection with torsion, is introduced; this connection is Ricci-flat if and only if M is an Einstein manifold.

On Horizontal and Complete Lifts of $(1,1)\;$ Tensor Fields F Satisfying ${f(2K+S,S)=0}$

2016 ◽  
Vol 6 (1) ◽  
pp. 143
Author(s):  
Abhishek Singh ◽  
Ramesh Kumar Pandey ◽  
Sachin Khare
Keyword(s):  
Tensor Fields

On Kenmotsu manifolds admitting a special type of semi-symmetric non-metric $\phi-$ connection

2018 ◽  
Vol 48 (1) ◽  
pp. 47-60
Author(s):  
Pradip Majhi ◽  
Ajit Barman ◽  
Uday Chand De
Keyword(s):  
Kenmotsu Manifolds

A note on invariant submanifolds of CR-integrable almost Kenmotsu manifolds

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6211-6218 ◽  
Author(s):  
Young Suh ◽  
Krishanu Mandal ◽  
Uday De
Keyword(s):  
Invariant Submanifold ◽  
Kenmotsu Manifold ◽  
Totally Geodesic ◽  
Almost Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Invariant Submanifolds

The present paper deals with invariant submanifolds of CR-integrable almost Kenmotsu manifolds. Among others it is proved that every invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold with k < -1 is totally geodesic. Finally, we construct an example of an invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold which is totally geodesic.

Pointwise pseudo-slant submanifolds of a Kenmotsu manifold

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5833-5853 ◽  
Author(s):  
Viqar Khan ◽  
Mohammad Shuaib
Keyword(s):  
Present Article ◽  
Warped Product ◽  
Shape Operator ◽  
Warped Products ◽  
Canonical Structure ◽  
Slant Submanifold ◽  
Kenmotsu Manifold ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds

In the present article, we have investigated pointwise pseudo-slant submanifolds of Kenmotsu manifolds and have sought conditions under which these submanifolds are warped products. To this end first, it is shown that these submanifolds can not be expressed as non-trivial doubly warped product submanifolds. However, as there exist non-trivial (single) warped product submanifolds of a Kenmotsu manifold, we have worked out characterizations in terms of a canonical structure T and the shape operator under which a pointwise pseudo slant submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

Spacetime symmetries

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Riemannian Manifold ◽  
Conservation Laws ◽  
Vector Fields ◽  
Killing Vector ◽  
Geodesic Equation ◽  
Spacetime Symmetries ◽  
Tensor Fields ◽  
Killing Vector Fields ◽  
Covariant Derivatives ◽  
Killing Equation

This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

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