Homogeneous manifolds with nonpositive curvature operator

1991 ◽  
Vol 37 (3) ◽  
Author(s):  
ThomasH. Wolter
Keyword(s):  
Nonpositive Curvature ◽  
Curvature Operator ◽  
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.

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

The Kobayashi-pseudodistance on homogeneous manifolds

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

scholarly journals Two-Point Homogeneous Manifolds

1965 ◽  
Vol 68 ◽  
pp. 746-753 ◽  
Author(s):  
H.O. Singh Varma
Keyword(s):  
Homogeneous Manifolds
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