H-contact unit tangent sphere bundles of Riemannian manifolds

Nikolayevsky, Yuri; Park, Jeong Hyeong

doi:10.1016/j.difgeo.2016.09.002

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…A contact metric manifold whose characteristic vector field ξ is a harmonic vector field is called an H-contact manifold. Nikolayevsky and Park [13] showed that for a Riemannian manifold M, T 1 M equipped with the standard contact metric structure is H-contact if and only if M is 2-stein. Gilkey, Swann, and Vanhecke [10] showed that a 4-dimensional manifold M is 2-stein if and only if locally there is a choice of orientation of M for which the metric is self-dual and Einstein ([10, Theorem 2.6]).…”

Section: Introductionmentioning

confidence: 99%

Curvature identities for Einstein manifolds of dimension 5 and 6

Euh¹,

Kim²,

Park³

2022

Preprint

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Patterson discussed the curvature identities on Riemannian manifolds in [14], and a curvature identity for any 6-dimensional Riemannian manifold was independently derived from the Chern-Gauss-Bonnet Theorem [8]. In this paper, we provide the explicit formulae of Patterson's curvature identity that holds on 5-dimensional and 6-dimensional Einstein manifolds. We confirm that the curvature identities on the Einstein manifold from the previous work [8] are the same as the curvature identities deduced from Patterson's result. We also provide examples that support the theorems.

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Section: Introductionmentioning

confidence: 99%

Curvature identities for Einstein manifolds of dimension 5 and 6

Euh¹,

Kim²,

Park³

2022

Preprint

Self Cite

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“…, where R X : T x M → T x M is the Jacobi operator (for further properties of 2-stein manifolds see [N3,NP]).…”

Section: Introductionmentioning

confidence: 99%

Totally geodesic submanifolds of Damek-Ricci spaces and Einstein hypersurfaces of the Cayley projective plane

Kim,

Nikolayevsky,

Park

2019

Preprint

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We classify totally geodesic submanifolds of Damek-Ricci spaces and show that they are either homogeneous (such submanifolds are known to be "smaller" Damek-Ricci spaces) or isometric to rank-one symmetric spaces of negative curvature. As a by-product, we obtain that a totally geodesic submanifold of any known harmonic manifold is by itself harmonic. We prove that the Cayley hyperbolic plane admits no Einstein hypersurfaces and that the only Einstein hypersurfaces in the Cayley projective plane are geodesic spheres of a particular radius; this completes the classification of Einstein hypersurfaces in rank-one symmetric spaces. We also show that if a 2-stein space admits a 2-stein hypersurface, then both are of constant curvature, under some additional conditions.

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Taut contact circles and bi-contact metric structures on three-manifolds

Perrone

2017

Ann Glob Anal Geom

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H-contact unit tangent sphere bundles of Riemannian manifolds

Cited by 4 publications

References 15 publications

Curvature identities for Einstein manifolds of dimension 5 and 6

Curvature identities for Einstein manifolds of dimension 5 and 6

Totally geodesic submanifolds of Damek-Ricci spaces and Einstein hypersurfaces of the Cayley projective plane

Taut contact circles and bi-contact metric structures on three-manifolds

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