On a new family of homogeneous Einstein manifolds

Eugene D. Rodionov

Displaying similar documents to “On a new family of homogeneous Einstein manifolds”

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 $S U (2) \times S U (2) / S O {(2)}_{r} (r \in Q, | r | \neq 1)$ 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 $V_{2} 𝐑^{n}$ .

Comparison of metrics on three-dimensional Lie groups

Federico G. Lastaria (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study local equivalence of left-invariant metrics with the same curvature on Lie groups $G$ and $\bar{G}$ of dimension three, when $G$ is unimodular and $\bar{G}$ is non-unimodular.