The Kobayashi-pseudodistance on homogeneous manifolds

1990 ◽  
Vol 68 (1) ◽  
pp. 117-134 ◽  
Author(s):  
Jörg Winkelmann
Keyword(s):  
Homogeneous Manifolds ◽  
Kobayashi Pseudodistance

Four-dimensional homogeneous manifolds satisfying some Einstein-like conditions

2020 ◽  
Vol 43 (3) ◽  
pp. 465-488
Author(s):  
Eduardo García-Río ◽  
Ali Haji-Badali ◽  
Rodrigo Mariño-Villar ◽  
M. Elena Vázquez-Abal
Keyword(s):  
Homogeneous Manifolds

Eigenvalues of the Curvature Operator for Certain Homogeneous Manifolds

1990 ◽  
Vol 42 (6) ◽  
pp. 981-999
Author(s):  
J. E. D'Atri ◽  
I. Dotti Miatello
Keyword(s):  
Riemannian Manifold ◽  
Tangent Space ◽  
Orthonormal Basis ◽  
Riemann Tensor ◽  
Inner Product ◽  
Curvature Operator ◽  
Curvature Function ◽  
Homogeneous Manifolds ◽  
Exterior Power ◽  
Image Position

Given a Riemannian manifold M, the Riemann tensor R induces the curvature operator on the exterior power of the tangent space, defined by the formula where the inner product is defined by From the symmetries of R, it follows that ρ is self-adjoint and so has only real eigenvalues. R also induces the sectional curvature function K on 2-planes in is an orthonormal basis of the 2-plane π.

scholarly journals On homogeneous manifolds whose isotropy actions are polar

2018 ◽  
Vol 161 (1-2) ◽  
pp. 15-34
Author(s):  
José Carlos Díaz-Ramos ◽  
Miguel Domínguez-Vázquez ◽  
Andreas Kollross
Keyword(s):  
Homogeneous Manifolds

scholarly journals Constant mean curvature spheres in homogeneous three-manifolds

2020 ◽  
Author(s):  
William H. Meeks ◽  
Pablo Mira ◽  
Joaquín Pérez ◽  
Antonio Ros
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Three Dimensional ◽  
Complete Classification ◽  
Homogeneous Manifolds ◽  
The Mean

Abstract We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.

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