scholarly journals Infinitesimal variations of invariant submanifolds of a Sasakian manifold

1978 ◽  
Vol 1 (2) ◽  
pp. 219-236 ◽  
Author(s):  
Kentaro Yano ◽  
U-Hang Ki ◽  
Jin Suk Pak
Keyword(s):  
Sasakian Manifold ◽  
Invariant Submanifolds

On semi-invariant submanifolds of a nearly Sasakian manifold admitting a semi-symmetric non-metric connection

2011 ◽  
Vol 17 (1) ◽  
Author(s):  
Lovejoy S. Das ◽  
Mobin Ahmad ◽  
Abdul Haseeb
Keyword(s):  
Sasakian Manifold ◽  
Metric Connection ◽  
Invariant Submanifolds ◽  
Nearly Sasakian

On Invariant Submanifolds of a Nearly Trans-Sasakian Manifold

2011 ◽  
Vol 36 (3) ◽  
pp. 423-429
Author(s):  
A. Turgut Vanli ◽  
R. Sari
Keyword(s):  
Sasakian Manifold ◽  
Invariant Submanifolds

scholarly journals Invariant Submanifolds in a Indefinite Trans-Sasakian Manifold

2016 ◽  
Vol 12 (04) ◽  
pp. 07-10
Author(s):  
Nanditha S Matad
Keyword(s):  
Sasakian Manifold ◽  
Invariant Submanifolds

scholarly journals TOTALLY UMBILICAL SEMI-INVARIANT SUBMANIFOLDS AND CR-SUBMANIFOLDS OF A SASAKIAN MANIFOLD

1993 ◽  
Vol 24 (2) ◽  
pp. 161-172
Author(s):  
S. M. KHURSEED HAIDER ◽  
V. A. KHAN ◽  
S. I. HUSAIN
Keyword(s):  
Space Form ◽  
Sasakian Manifold ◽  
Classification Theorem ◽  
Sasakian Space Form ◽  
Invariant Submanifold ◽  
Totally Umbilical ◽  
Cr Submanifold ◽  
Invariant Submanifolds ◽  
Cr Submanifolds

In the present paper, a classification theorem for totally um- bilical semi-invariant submanifold is established. CR-submanifolds of a Sasakian space form are studied in detail, and finally a theorem for a CR- submanifold of a Sasakian manifold to be a proper contact CR-product is proved.

scholarly journals Skew semi-invariant submanifolds of generalized quasi-Sasakian manifolds

2018 ◽  
Vol 9 (2) ◽  
pp. 188-197 ◽  
Author(s):  
M.D. Siddiqi ◽  
A. Haseeb ◽  
M. Ahmad
Keyword(s):  
Sasakian Manifold ◽  
Equivalence Relations ◽  
Cr Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
New Class ◽  
Almost Contact Metric ◽  
Invariant Submanifolds

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.

scholarly journals Semi-invariant submanifolds of Lorentzian Sasakian manifolds

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Pablo Alegre
Keyword(s):  
Space Form ◽  
Contact Manifold ◽  
Sasakian Manifold ◽  
Sasakian Space Form ◽  
Sasakian Manifolds ◽  
Principal Characteristics ◽  
Almost Contact Manifold ◽  
Invariant Submanifolds

AbstractIn this paper we introduce the notion of semi-invariant submanifolds of a Lorentzian almost contact manifold. We study their principal characteristics and the particular cases in which the manifold is a Lorentzian Sasakian manifold or a Lorentzian Sasakian space form.

Totally umbilical semi-invariant submanifolds of a nearly trans-Sasakian manifold

2007 ◽  
pp. 67-74 ◽  
Author(s):  
V. Khan ◽  
M. Khan ◽  
S. Uddin
Keyword(s):  
Sasakian Manifold ◽  
Totally Umbilical ◽  
Invariant Submanifolds

scholarly journals ON AN INVARIANT SUBMANIFOLD OF HYPERBOLIC SASAKIAN MANIFOLDS

2017 ◽  
pp. 353
Author(s):  
Shravan Kumar Pandey ◽  
Ram Nawal Singh
Keyword(s):  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Totally Geodesic ◽  
Invariant Submanifolds

The object of the present paper is to study an invariant submanifold of hyperbolic Sasakian maifolds. In this paper, we consider semiparallel and 2-semiparallel invariant submanifolds of hyperbolic Sasakian manifold and it is shown that these submanifolds are totally geodesic. It is also proved that on an invariant submanifold of hyperbolic Sasakian manifolds the conditions $I(X, Y).\alpha = 0$, $I(X, Y).\tilde{\nabla}\alpha = 0$, $C(X, Y).\alpha = 0$, $C(X, Y).\tilde{nabla}\alpha = 0$ holds if and only if it is totally geodesic.

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