On normal homogeneous Einstein manifolds

McKenzie Y. Wang; Wolfgang Ziller

Displaying similar documents to “On normal 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 $V_{2} 𝐑^{n}$ .

Homogeneous Einstein metrics on flag manifolds.

Sakane, Y. (1999)

Lobachevskii Journal of Mathematics

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New examples of Einstein metrics in dimension four.

Ghanam, Ryad (2010)

International Journal of Mathematics and Mathematical Sciences

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Non-standard Einstein extensions of five dimensional nilpotent metric Lie algebras.

Nikitenko, E.V (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Selfdual Einstein hermitian four-manifolds

Vestislav Apostolov, Paul Gauduchon (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We provide a local classification of selfdual Einstein riemannian four-manifolds admitting a positively oriented hermitian structure and characterize those which carry a hyperhermitian, non-hyperkähler structure compatible with the negative orientation. We show that selfdual Einstein 4-manifolds obtained as quaternionic quotients of $ℍ P^{2}$ and $ℍ H^{2}$ are hermitian.