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Displaying similar documents to “Einstein equation for an invariant metric on generalized flag manifolds and inner automorphisms.”

Einstein metrics on a class of five-dimensional homogeneous spaces

Eugene D. Rodionov (1991)

Commentationes Mathematicae Universitatis Carolinae

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We prove that there is exactly one homothety class of invariant Einstein metrics in each space S U ( 2 ) × S U ( 2 ) / S O ( 2 ) r ( r Q , | r | 1 ) defined below.

Homogeneous Einstein metrics on Stiefel manifolds

Andreas Arvanitoyeorgos (1996)

Commentationes Mathematicae Universitatis Carolinae

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A Stiefel manifold V k 𝐑 n is the set of orthonormal k -frames in 𝐑 n , and it is diffeomorphic to the homogeneous space S O ( n ) / S O ( n - k ) . We study S O ( n ) -invariant Einstein metrics on this space. We determine when the standard metric on S O ( n ) / S O ( n - k ) is Einstein, and we give an explicit solution to the Einstein equation for the space V 2 𝐑 n .