scholarly journals Nearly Kähler manifolds with positive holomorphic sectional curvature

1985 ◽  
Vol 8 (2) ◽  
pp. 139-156
Author(s):  
Kouei Sekigawa ◽  
Takuji Sato
Keyword(s):  
Sectional Curvature ◽  
Kähler Manifolds ◽  
Holomorphic Sectional Curvature ◽  
Kahler Manifolds ◽  
Nearly Kähler ◽  
Nearly Kähler Manifolds

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 Toric nearly Kähler manifolds

2019 ◽  
Vol 55 (4) ◽  
pp. 703-717 ◽  
Author(s):  
Andrei Moroianu ◽  
Paul-Andi Nagy
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Nearly Kähler ◽  
Nearly Kähler Manifolds

On the Kähler-likeness on nearly Kähler manifolds

2020 ◽  
pp. 2150132
Author(s):  
Masaya Kawamura
Keyword(s):  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Hermitian Metrics ◽  
Kahler Manifold ◽  
Nearly Kähler ◽  
Nearly Kähler Manifolds ◽  
Nearly Kähler Manifold

We introduce Kähler-like, G-Kähler-like almost Hermitian metrics. We characterize the Kähler-likeness and the G-Kähler-likeness, and show that these properties are equivalent on nearly Kähler manifolds. Furthermore, we prove that a nearly Kähler manifold with the Kähler-likeness is Kähler.

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