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Author(s):  
Mehmet Atc̣eken

AbstractIn the present paper, we study invariant submanifolds of almost Kenmotsu structures whose Riemannian curvature tensor has $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -nullity distribution. Since the geometry of an invariant submanifold inherits almost all properties of the ambient manifold, we research how the functions $$\kappa ,\mu $$ κ , μ and $$\nu $$ ν behave on the submanifold. In this connection, necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -space to be totally geodesic under some conditions.


2021 ◽  
Vol 13(62) (2) ◽  
pp. 545-560
Author(s):  
Sujoy Ghosh ◽  
Avijit Sarkar

The object of the present paper is to deduce some necessary and sufficient conditions for invariant Submanifolds of paracontact (κ, µ)-spaces to be totally geodesic. We also establish that a totally umbilical invariant submanifold of a paracontact (κ, µ)-manifold is also totally geodesic. Some more necessary and sufficient conditions for a submanifold of a paracontact (κ, µ)-manifold to be totally geodesic have been deduced using parallelity and pseudo parallelity of the second fundamental form. In the last section we obtain some results on paracontact (κ, µ)-manifold with concircular canonical field.


Author(s):  
Mustafa Gök ◽  
Erol Kılıç

AbstractIn this paper, we investigate any non-invariant submanifold of a locally decomposable golden Riemannian manifold in the case that the rank of the set of tangent vector fields of the induced structure on the submanifold by the golden structure of the ambient manifold is less than or equal to the codimension of the submanifold.


Author(s):  
Gajendra Singh

In the present paper we have obtained some properties of an almost semi-invariant of a normal almost paracontact manifold. The integrability condition of distributions  have also been discussed. According to these cases normal almost paracontact manifold is categorized and its used to demonstrate that the method presented in this paper is effective.


2020 ◽  
Vol 5 (1) ◽  
pp. 283-292
Author(s):  
Ramazan Sari

AbstractIn this paper different curvature tensors on Lorentzian Kenmotsu manifod are studied. We investigate constant ϕ–holomorphic sectional curvature and ℒ-sectional curvature of Lorentzian Kenmotsu manifolds, obtaining conditions for them to be constant of Lorentzian Kenmotsu manifolds in such condition. We calculate the Ricci tensor and scalar curvature for all the cases. Moreover we investigate some properties of semi invariant submanifolds of a Lorentzian Kenmotsu space form. We show that if a semi-invariant submanifold of a Lorentzian Kenmotsu space form M is totally geodesic, then M is an η−Einstein manifold. We consider sectional curvature of semi invariant product of a Lorentzian Kenmotsu manifolds.


Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 313
Author(s):  
L.P. Horwitz ◽  
R.I. Arshansky

We show that in a relativistically covariant formulation of the two-body problem, the bound state spectrum is in agreement, up to relativistic corrections, with the non-relativistic bound-state spectrum. This solution is achieved by solving the problem with support of the wave functions in an O ( 2 , 1 ) invariant submanifold of the Minkowski spacetime. The O ( 3 , 1 ) invariance of the differential equation requires, however, that the solutions provide a representation of O ( 3 , 1 ) . Such solutions are obtained by means of the method of induced representations, providing a basic insight into the subject of the symmetries of relativistic dynamics.


Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1209 ◽  
Author(s):  
Mustafa Gök ◽  
Sadık Keleş ◽  
Erol Kılıç

In this paper, we study some characterizations for any submanifold of a golden Riemannian manifold to be semi-invariant in terms of canonical structures on the submanifold, induced by the golden structure of the ambient manifold. Besides, we determine forms of the distributions involved in the characterizations of a semi-invariant submanifold on both its tangent and normal bundles.


2018 ◽  
Vol 9 (2) ◽  
pp. 188-197 ◽  
Author(s):  
M.D. Siddiqi ◽  
A. Haseeb ◽  
M. Ahmad

In the present paper,  we study a new class of submanifolds of a generalized Quasi-Sasakian manifold, called skew semi-invariant submanifold. We obtain integrability conditions of the distributions on a skew semi-invariant submanifold and also find the condition for a skew semi-invariant submanifold  of a generalized Quasi-Sasakian manifold to be mixed totally geodesic. Also it is shown that a  skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold will be anti-invariant if and only if $A_{\xi}=0$; and the submanifold will be skew semi-invariant submanifold if $\nabla w=0$. The equivalence relations for the  skew semi-invariant submanifold of a  generalized Quasi-Sasakian manifold are given. Furthermore, we have proved that a skew semi-invariant $\xi^\perp$-submanifold of a normal almost contact metric manifold and a generalized Quasi-Sasakian manifold with non-trivial invariant distribution is $CR$-manifold. An example of dimension 5 is given to show that a skew semi-invariant $\xi^\perp$ submanifold is a $CR$-structure on the manifold.


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