scholarly journals Algebras of curvature forms on homogeneous manifolds

1999 ◽  
pp. 227-235 ◽  
Author(s):  
Alexander Postnikov ◽  
Boris Shapiro ◽  
Mikhail Shapiro
Keyword(s):  
Homogeneous Manifolds

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
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