Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds

2019 ◽  
Vol 130 ◽  
pp. 347-374
Author(s):  
E. Calviño-Louzao ◽  
X. García-Martínez ◽  
E. García-Río ◽  
I. Gutiérrez-Rodríguez ◽  
R. Vázquez-Lorenzo
Keyword(s):  
Homogeneous Manifolds ◽  
Bach Flat

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.

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