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 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 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 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.

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 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 CR-submanifolds of a Kaehler manifold. I

1981 ◽  
Vol 16 (2) ◽  
pp. 305-322 ◽  
Author(s):  
Bang-yen Chen
Keyword(s):  
Kaehler Manifold ◽  
Cr Submanifolds

scholarly journals On totally umbilicalCR-submanifolds of a Kaehler manifold

1993 ◽  
Vol 16 (2) ◽  
pp. 405-408
Author(s):  
M. A. Bashir
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Curvature Vector ◽  
Lens Space ◽  
Holomorphic Sectional Curvature ◽  
Mean Curvature Vector ◽  
Kaehler Manifold ◽  
Totally Umbilical ◽  
The Mean

LetMbe a compact3-dimensional totally umbilicalCR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector ofMdoes not vanish, thenMis either diffeomorphic toS3orRP3or a lens spaceLp,q3.

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