Compact homogeneous Einstein 6-manifolds

Nikonorov, Yu. G.; Rodionov, E. D.

doi:10.1016/s0926-2245(03)00051-2

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Introduction4

N > 16 Solutions With N R =1

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2018

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Cited by 22 publications

(39 citation statements)

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“…There is a 6-dimensional compact homogeneous Einstein Riemannian manifold, that is not geodesic orbit. This is a flag manifold SU (3)/T max with a Kähler-Einstein invariant metric (it is different from the SU (3)-normal one), see details e. g. in [26]. The fact that it is not geodesic orbit follows also from the results of [19].…”

Section: Introductionmentioning

confidence: 99%

On Left-Invariant Einstein Riemannian Metrics That Are Not Geodesic Orbit

Nikonorov

2018

Transformation Groups

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In this paper we prove that the compact Lie group G2 admits a left-invariant Einstein metric that is not geodesic orbit. In order to prove the required assertion, we develop some special tools for geodesic orbit Riemannian manifolds. It should be noted that a suitable metric is discovered in a recent paper by I. Chrysikos and Y. Sakane, where the authors proved also that this metric is not naturally reductive.2010 Mathematical Subject Classification: 53C20, 53C25, 53C35.

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Section: Introductionmentioning

confidence: 99%

On Left-Invariant Einstein Riemannian Metrics That Are Not Geodesic Orbit

Nikonorov

2018

Transformation Groups

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“…Alekseevsky classified homogeneous Einstein 5-manifolds with negative sectional curvature [6]. In [7] a partial classification theorem for compact homogeneous Einstein 6-manifolds was announced; a complete version of this article will appear soon [8].…”

Section: Introductionmentioning

confidence: 99%

Compact Homogeneous Einstein 7-Manifolds

Nikonorov¹

2004

Geom Dedicata

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“…where λ r is a complex frame,λ r = λr, on S 6 and ℓ 7 is a left-invariant frame on S 1 . The invariant forms on S 6 are the 2-form 30) and the holomorphic 3-form The most general invariant metric on M 7 is…”

Section: N > 16 Solutions With N R =mentioning

confidence: 99%