On Eta-Einstein Sasakian Geometry

By Charles P. Boyer, Krzysztof Galicki, P. Matzeu. 2004

159 citations recorded by the source corpus.

A compact quasi-regular Sasakian manifold M is foliated by one-dimensional leaves and the transverse space of this characteristic foliation is necessarily a compact Kähler orbifold . In the case when the transverse space is also Einstein the corresponding Sasakian manifold M is said to be Sasakian η-Einstein. In this article we study η-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem in the context of Sasakian geometry to prove the existence of η-Einstein structures on many different compact manifolds, including exotic spheres. We also relate these results to the existence of Einstein-Weyl and Lorenzian Sasakian-Einstein structures.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f268795870abe2c64914797c01819ee12e510426

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In Applied Mathematics

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

A class of Sasakian 5-manifolds (2008, unknown): “When the Ricci curvature tensor is given by Ricg = λg + ν α ⊗ α, for some constants λ, ν ∈ R, the Sasakian structure is called α-Einstein ([23, 29, 8]).”
Sasaki–Einstein Manifolds and Volume Minimisation (2006, background): “8 This is a transverse homothety, in the language of Boyer and Galicki [38].”