NEARLY COSYMPLECTIC MANIFOLD OF HOLOMORPHIC SECTIONAL CURVATURE TENSOR

2018 ◽  
Vol 106 (1) ◽  
pp. 171-181 ◽  
Author(s):  
Habeeb M. Abood ◽  
Nawaf J. Mohammed
Keyword(s):  
Sectional Curvature ◽  
Curvature Tensor ◽  
Holomorphic Sectional Curvature ◽  
Cosymplectic Manifold ◽  
Nearly Cosymplectic

scholarly journals Some Results on Projective Curvature Tensor of Nearly Cosymplectic Manifold

2018 ◽  
Vol 11 (3) ◽  
pp. 823-833 ◽  
Author(s):  
Nawaf Jaber Mohammed ◽  
Habeeb Mtashar Abood
Keyword(s):  
Curvature Tensor ◽  
Einstein Space ◽  
Geometric Meaning ◽  
Cosymplectic Manifold ◽  
Projective Curvature ◽  
Projective Tensor ◽  
Nearly Cosymplectic ◽  
Projective Curvature Tensor

In the nearly cosymplectic manifold, dened a tensor of type (4,0), it's called a projective curvature tensor. In this article we discuss an interesting question; what the geometric meaning of this tensor when it's act on nearly cosymplectic manifold? The answer of this question leads to get an application on Einstein space. In particular, the necessary and sucient conditions that a projective tensor is vanishes are found.

scholarly journals Curvature Identities for Generalized Kenmotsu Manifolds

2021 ◽  
Vol 244 ◽  
pp. 09005
Author(s):  
Abu-Saleem Ahmad ◽  
Ivan Kochetkov ◽  
Aligadzhi Rustanov
Keyword(s):  
Sectional Curvature ◽  
Curvature Tensor ◽  
Structure Tensor ◽  
Holomorphic Sectional Curvature ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Kenmotsu Manifolds ◽  
Analytic Expression ◽  
Local Characterization

In the present paper we obtained 2 identities, which are satisfied by Riemann curvature tensor of generalized Kenmotsu manifolds. There was obtained an analytic expression for third structure tensor or tensor of f-holomorphic sectional curvature of GK-manifold. We separated 2 classes of generalized Kenmotsu manifolds and collected their local characterization.

scholarly journals On a $K$-space of constant holomorphic sectional curvature

1973 ◽  
Vol 25 (3) ◽  
pp. 297-306 ◽  
Author(s):  
Yoshiyuki Watanabe ◽  
Kichiro Takamatsu
Keyword(s):  
Sectional Curvature ◽  
Holomorphic Sectional Curvature

Jacobi fields and geodesic spheres

1979 ◽  
Vol 82 (3-4) ◽  
pp. 233-240 ◽  
Author(s):  
L. Vanhecke ◽  
T. J. Willmore
Keyword(s):  
Sectional Curvature ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Holomorphic Sectional Curvature ◽  
Principal Curvatures ◽  
Jacobi Fields ◽  
Geodesic Spheres ◽  
Jacobi Vector ◽  
Nearly Kähler ◽  
Nearly Kähler Manifolds

SynopsisThis is a contribution to the general problem of determining the extent to which the geometry of a riemannian manifold is determined by properties of its geodesic spheres. In particular we show that total umbilicity of geodesic spheres determines riemannian manifolds of constant sectional curvature; quasi-umbilicity of geodesic spheres determines Kähler and nearly-Kähler manifolds of constant holomorphic sectional curvature; and the condition that geodesic spheres have only two different principal curvatures, one having multiplicity 3, determines manifolds locally isometric to the quaternionic projective spaces. The use of Jacobi vector fields leads to a unified treatment of these different cases.

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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