New examples of homogeneous Einstein metrics.

Kerr, Megan M.

doi:10.1307/mmj/1030132086

Cited by 43 publications

(40 citation statements)

References 6 publications

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“…The same result was independently found by Kerr [15]. For m = 2, the group SO(3) has also a unique Einstein metric, but for m = 3, the Stiefel manifold V 2 R 4 = SO(4)/SO(2) admits exactly two SO(4)-invariant Einstein metrics [11] (cf.…”

Section: Theorem 1 ([7])supporting

confidence: 75%

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On Einstein Riemannian g-natural metrics on unit tangent sphere bundles

Abbassi

Kowalski

2010

Ann Glob Anal Geom

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We prove that there is always a locally homogeneous Einstein g-natural metric on the unit tangent sphere bundle over any Riemannian space of constant positive sectional curvature. Furthermore, using the (1-1) correspondence between all SO(m + 1)-invariant homogeneous metrics on the Stiefel manifold V 2 R m+1 = SO(m + 1)/SO(m − 1) and all g-natural metrics on T 1 S m (Abbassi and Kowalski, Diff. Geom. Appl., to appear [7]), we reconstruct, by purely local procedure, the same well-known unique SO(m + 1)-invariant homogeneous Einstein metric on V 2 R m+1 , m = 3, initially constructed by Kobayashi.

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Section: Theorem 1 ([7])supporting

confidence: 75%

“…Let us start our section by the following result from Abbassi and Kowalski [7] Proposition 3 Every Riemannian SO(m + 1)-invariant metric on the Stiefel manifold In the article by Megan Kerr [15], the author uses parameters x 0 , x 1 , x 2 , x 3 …”

Section: Einstein Riemannian G-natural Metrics On T 1 Mmentioning

confidence: 99%

On Einstein Riemannian g-natural metrics on unit tangent sphere bundles

Abbassi

Kowalski

2010

Ann Glob Anal Geom

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“…Any other G-invariant metric on G/K can be written as Q (L·, ·) where L is a positive-definite symmetric Ad(K )-equivariant linear map [13]. That is, L : p → p. The space of Ad(K )-invariant scalar products is parameterized by the matrices L. Finally, the one parameter family of homogeneous metrics, g t , can be written as…”

Section: Diagonalizability and The Monotypic Casementioning

confidence: 99%

“…The space of intertwining maps is 1-dimensional in the orthogonal case, 2-dimensional in the unitary case, and 4-dimensional in the symplectic case [13]. Below, we consider each of these cases separately.…”

Section: The Case Of Two Equivalent Summandsmentioning

confidence: 99%

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Diagonalizing cohomogeneity-one Einstein metrics

Dammerman¹

2009

Journal of Geometry and Physics

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a b s t r a c tWe investigate when it is possible to globally diagonalize an Einstein metric of cohomogeneity-one under the action of a compact connected Lie group G with isotropy subgroup K . Restricting our attention to the non-monotypic case in which cohomogeneityone metrics are not automatically diagonalizable, we make use of a subset of the ODEs of the Einstein condition to globally diagonalize the Einstein metric in certain cases. The program we use is inspired by a result well-known to relativists which states that Einstein metrics must be diagonalizable in the Bianchi IX case. We present a full classification of all the cohomogeneity-one metrics on which this method can be used.

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Standard homogeneous (α1,α2)${\big(\alpha _1,\alpha _2\big)}$‐metrics and geodesic orbit property

Zhang

2022

Mathematische Nachrichten

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New examples of homogeneous Einstein metrics.

Cited by 43 publications

References 6 publications

On Einstein Riemannian g-natural metrics on unit tangent sphere bundles

On Einstein Riemannian g-natural metrics on unit tangent sphere bundles

Diagonalizing cohomogeneity-one Einstein metrics

Standard homogeneous (α1,α2)${\big(\alpha _1,\alpha _2\big)}$‐metrics and geodesic orbit property

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