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 TOTALLY UMBILICAL CR-SUBMANIFOLDS OF A KAEHLER MANIFOLD

1993 ◽  
Vol 24 (1) ◽  
pp. 43-49
Author(s):  
S. M. KHURSHEED HAIDER ◽  
V. A. KHAN ◽  
S . I. HUSAIN
Keyword(s):  
Classification Theorem ◽  
Kaehler Manifold ◽  
Totally Umbilical ◽  
Cr Submanifold ◽  
Cr Submanifolds

In the present paper we study totally umbilical CR-submanifolds of a Kaehler manifold. A classification theorem for a $D^\perp$-totally umbilical CR-submanifold is proved. The conditions under which a CR- submanifold becomes a CR-product are obtained, and finally a theorem for a CR-submanifold to be a proper CR-product is also established.

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.

scholarly journals Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Dae Ho Jin
Keyword(s):  
Vector Field ◽  
Space Form ◽  
Sasakian Manifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Structure ◽  
Sasakian Space Forms ◽  
Generalized Sasakian Space Form ◽  
Characterization Theorems ◽  
Lightlike Hypersurfaces

We study lightlike hypersurfacesMof an indefinite generalized Sasakian space formM-(f1,f2,f3), with indefinite trans-Sasakian structure of type(α,β), subject to the condition that the structure vector field ofM-is tangent toM. First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type(α,β). Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form.

scholarly journals TOTALLY UMBILICAL CR-SUBMANIFOLDS OF A NEARLY KAEHLER MANIFOLD

1996 ◽  
Vol 27 (2) ◽  
pp. 145-149
Author(s):  
S. H. KON ◽  
SIN-LENG TAN
Keyword(s):  
Kaehler Manifold ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Cr Submanifold ◽  
Nearly Kaehler Manifold ◽  
Totally Real ◽  
Cr Submanifolds

The geometry of a CR-submanifold in a Kaehler manifold has been extensively studied. B.Y . Chen has classified the totally umbilical CR-submanifolds of a Kaehler manifold and showed that they are either totally geodesic, or totally real or dim$(D^{\perp}) =1$. In this paper we show that such a result is also true in a nearly Kaehler manifold.

scholarly journals Semi-invariant submanifolds of a Sasakian space form

1984 ◽  
Vol 48 (2) ◽  
pp. 229-240 ◽  
Author(s):  
Aurel Bejancu ◽  
Neculai Papaghiuc
Keyword(s):  
Space Form ◽  
Sasakian Space Form ◽  
Invariant Submanifolds

scholarly journals CERTAIN CLASS OF CONTACT CR-SUBMANIFOLDS OF A SASAKIAN SPACE FORM

2014 ◽  
Vol 29 (1) ◽  
pp. 131-140
Author(s):  
Hyang Sook Kim ◽  
Don Kwon Choi ◽  
Jin Suk Pak
Keyword(s):  
Space Form ◽  
Sasakian Space Form ◽  
Cr Submanifolds

scholarly journals On contact CR-submanifolds of sasakian manifolds

1983 ◽  
Vol 6 (2) ◽  
pp. 313-326
Author(s):  
Koji Matsumoto
Keyword(s):  
Space Form ◽  
Sasakian Manifold ◽  
Second Fundamental Form ◽  
Sasakian Space Form ◽  
Sasakian Manifolds ◽  
Fundamental Properties ◽  
The Second Fundamental Form ◽  
Ambient Manifold ◽  
The One ◽  
Kaehlerian Manifold

Recently, K.Yano and M.Kon [5] have introduced the notion of a contactCR-submanifold of a Sasakian manifold which is closely similar to the one of aCR-submanifold of a Kaehlerian manifold defined by A. Bejancu [1].In this paper, we shall obtain some fundamental properties of contactCR-submanifolds of a Sasakian manifold. Next, we shall calculate the length of the second fundamental form of a contactCR-product of a Sasakian space form (THEOREM 7.4). At last, we shall prove that a totally umbilical contactCR-submanifold satisfying certain conditions is totally geodesic in the ambient manifold (THEOREM 8.1).

scholarly journals A note on Chen's basic equality for submanifolds in a Sasakian space form

2003 ◽  
Vol 2003 (11) ◽  
pp. 711-716 ◽  
Author(s):  
Mukut Mani Tripathi ◽  
Jeong-Sik Kim ◽  
Seon-Bu Kim
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Sectional Curvature ◽  
Space Form ◽  
Sasakian Space Form ◽  
Invariant Submanifold ◽  
Basic Equality

It is proved that a Riemannian manifoldMisometrically immersed in a Sasakian space formM˜(c)of constantφ-sectional curvaturec<1, with the structure vector fieldξtangent toM, satisfies Chen's basic equality if and only if it is a3-dimensional minimal invariant submanifold.

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