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 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 CR-SUBMANIFOLDS OF A QUASl-KAEHLER MANIFOLD

1995 ◽  
Vol 26 (3) ◽  
pp. 261-266
Author(s):  
S. H. KON ◽  
SIN-LENG TAN
Keyword(s):  
Sufficient Conditions ◽  
Kaehler Manifold ◽  
Complex Submanifold ◽  
Cr Submanifold ◽  
Almost Complex ◽  
Cr Submanifolds

Let $M$ be a CR-submanifold of a quasi-Kaehler manifold $N$. Sufficient conditions for the holomorphic distribution $D$ in $M$ to be integrable are derived. We also show that $D$ is minimal. It follows that an (almost) complex submanifold of a quasi-Kaehler manifold is minimal, this generalizes the well known result that a complex submanifold of a Kaehler manifold is minimal.

Geometric classification of warped product submanifolds of nearly Kaehler manifolds with a slant fiber

2019 ◽  
Vol 16 (02) ◽  
pp. 1950031 ◽  
Author(s):  
Akram Ali ◽  
Jae Won Lee ◽  
Ali H. Alkhaldi
Keyword(s):  
Warped Product ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Kaehler Manifold ◽  
Slant Submanifold ◽  
Riemannian Product ◽  
Slant Angle ◽  
Kaehler Manifolds ◽  
Nearly Kaehler Manifold ◽  
Totally Real

There are two types of warped product pseudo-slant submanifolds, [Formula: see text] and [Formula: see text], in a nearly Kaehler manifold. We derive an optimization for an extrinsic invariant, the squared norm of second fundamental form, on a nontrivial warped product pseudo-slant submanifold [Formula: see text] in a nearly Kaehler manifold in terms of a warping function and a slant angle when the fiber [Formula: see text] is a slant submanifold. Moreover, the equality is verified for depending on what [Formula: see text] and [Formula: see text] are, and also we show that if the equality holds, then [Formula: see text] is a simply Riemannian product. As applications, we prove that the warped product pseudo-slant submanifold has the finite Kinetic energy if and only if [Formula: see text] is a totally real warped product submanifold.

scholarly journals Totally umbilical CR-submanifolds of a Kaehler manifold

1986 ◽  
Vol 9 (3) ◽  
pp. 425-429 ◽  
Author(s):  
Sharief Deshmukh ◽  
S. I. Husain
Keyword(s):  
Kaehler Manifold ◽  
Totally Umbilical ◽  
Cr 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 Contact co-isotropic CR submanifolds of a pseudo-Sasakian manifold

1984 ◽  
Vol 7 (2) ◽  
pp. 339-350 ◽  
Author(s):  
Vladislav V. Goldberg ◽  
Radu Rosca
Keyword(s):  
Vertical Distribution ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Totally Geodesic ◽  
Isotropic Submanifold ◽  
Cr Submanifold ◽  
Necessary And Sufficient ◽  
Cr Submanifolds

It is proved that any co-isotropic submanifoldMof a pseudo-Sasakian manifoldM˜(U,ξ,η˜,g˜)is a CR submanifold (such submanfolds are called CICR submanifolds) with involutive vertical distributionν1. The leavesM1ofD1are isotropic andMisν1-totally geodesic. IfMis foliate, thenMis almost minimal. IfMis RicciD1-exterior recurrent, thenMreceives two contact Lagrangian foliations. The necessary and sufficient conditions forMto be totally minimal is thatMbe contactD1-exterior recurrent.

scholarly journals On Submersion of CR-Submanifolds of l.c.q.K. Manifold

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Majid Ali Choudhary ◽  
Mahmood Jaafari Matehkolaee ◽  
Mohd. Jamali
Keyword(s):  
Riemannian Submersion ◽  
Hermitian Manifold ◽  
Kaehler Manifold ◽  
Almost Hermitian Manifold ◽  
Cr Submanifold ◽  
Locally Conformal ◽  
Cr Submanifolds

We study submersion of CR-submanifolds of an l.c.q.K. manifold. We have shown that if an almost Hermitian manifold B admits a Riemannian submersion π:M→B of a CR-submanifold M of a locally conformal quaternion Kaehler manifold M¯, then B is a locally conformal quaternion Kaehler manifold.

scholarly journals Quaternion CR-submanifolds of a quaternion Kaehler manifold

2001 ◽  
Vol 27 (1) ◽  
pp. 27-37 ◽  
Author(s):  
Bassil J. Papantoniou ◽  
M. Hasan Shahid
Keyword(s):  
Kaehler Manifold ◽  
Cr Submanifold ◽  
Cr Submanifolds

We study the quaternion CR-submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR-submanifold.

scholarly journals Generic Submanifolds of Nearly Kaehler Manifolds with Certain Parallel Canonical Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Qingqing Zhu ◽  
Biaogui Yang
Keyword(s):  
Point Of View ◽  
Real Hypersurfaces ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Generic Submanifolds ◽  
Geometric Point ◽  
Complex Submanifolds ◽  
Generic Submanifold ◽  
Nearly Kaehler Manifold ◽  
Totally Real

The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds, and CR-submanifolds. In this paper we initiate the study of generic submanifolds in a nearly Kaehler manifold from differential geometric point of view. Some fundamental results in this paper will be obtained.

scholarly journals Concurrent Vector Fields on Lightlike Hypersurfaces

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 59
Author(s):  
Erol Kılıç ◽  
Mehmet Gülbahar ◽  
Ecem Kavuk
Keyword(s):  
Vector Fields ◽  
Ricci Soliton ◽  
Lorentzian Manifold ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Lightlike Hypersurfaces

Concurrent vector fields lying on lightlike hypersurfaces of a Lorentzian manifold are investigated. Obtained results dealing with concurrent vector fields are discussed for totally umbilical lightlike hypersurfaces and totally geodesic lightlike hypersurfaces. Furthermore, Ricci soliton lightlike hypersurfaces admitting concurrent vector fields are studied and some characterizations for this frame of hypersurfaces are obtained.

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