scholarly journals Totally real bisectional curvature, Bochner-Kaehler and Einstein-Kaehler manifolds

1999 ◽  
Vol 10 (2) ◽  
pp. 145-154 ◽  
Author(s):  
Bang-Yen Chen ◽  
Franki Dillen
Keyword(s):  
Bisectional Curvature ◽  
Kaehler Manifolds ◽  
Totally Real

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 On Sectional Curvatures of (ε)-Sasakian Manifolds

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
Rakesh Kumar ◽  
Rachna Rani ◽  
R. K. Nagaich
Keyword(s):  
Sectional Curvature ◽  
Curvature Tensor ◽  
Riemannian Curvature ◽  
Sasakian Manifolds ◽  
Bisectional Curvature ◽  
Riemannian Curvature Tensor ◽  
Sectional Curvatures ◽  
Totally Real

We obtain some basic results for Riemannian curvature tensor of (ε)-Sasakian manifolds and then establish equivalent relations amongφ-sectional curvature, totally real sectional curvature, and totally real bisectional curvature for (ε)-Sasakian manifolds.

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 Totally umbilicalCR-submanifolds of Semi-Riemannian Kaehler manifolds

1987 ◽  
Vol 10 (3) ◽  
pp. 551-555 ◽  
Author(s):  
K. L. Duggal ◽  
R. Sharma
Keyword(s):  
Second Fundamental Form ◽  
Kaehler Manifold ◽  
Normal Contact ◽  
Kaehler Manifolds ◽  
The Second Fundamental Form ◽  
Real Distribution ◽  
Contact Metric Structure ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Totally Real

We study totally umbilicalCR-submanifolds of a Kaehler manifold carrying a semi-Riemannian metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For dimension equal to one, we show, in particular, that they are endowed with a normal contact metric structure if and only if the second fundamental form is parallel.

scholarly journals THE DEGREE OF HOLOMORPHIC APPROXIMATION ON A TOTALLY REAL SET

2009 ◽  
Vol 79 (1) ◽  
pp. 171-176
Author(s):  
SAID ASSERDA
Keyword(s):  
Compact Support ◽  
Infinite Order ◽  
Holomorphic Functions ◽  
Degree Of Approximation ◽  
Gevrey Class ◽  
Bisectional Curvature ◽  
Bounded Geometry ◽  
Holomorphic Bisectional Curvature ◽  
Open Set ◽  
Totally Real

AbstractLet E be a totally real set on a Stein open set Ω on a complete noncompact Kähler manifold (M,g) with nonnegative holomorphic bisectional curvature such that (Ω,g) has bounded geometry at E. Then every function f in a Cp class with compact support on Ω and $\overline \partial $-flat on E up to order p−1,p≥2 (respectively, in a Gevrey class of order s>1, with compact support on Ω and $\overline \partial $-flat on E up to infinite order) can be approximated on compacts subsets of E by holomorphic functions fk on Ω with degree of approximation equal k−p/2 (respectively, exp (−c(s)k1/2(s−1)) ).

Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Locally Conformal ◽  
Totally Real ◽  
Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

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