Sasaki-Einstein and paraSasaki-Einstein metrics from (κ,μ)-structures

Abstract

We prove that any non-Sasakian contact metric (κ,μ)-space admits a canonical η-Einstein Sasakian or η-Einstein paraSasakian metric. An explicit expression for the curvature tensor fields of those metrics is given and we find the values of κand μfor which such metrics are Sasaki-Einstein and paraSasaki-Einstein. Conversely, we prove that, under some natural assumptions, a K-contact or K-paracontact manifold foliated by two mutually orthogonal, totally geodesic Legendre foliations admits a contact metric (κ,μ)-structure. Furthermore, we apply the above results to the geometry of tangent sphere bundles and we discuss some topological and geometrical properties of (κ,μ)-spaces related to the existence of Eistein-Weyl and Lorentzian Sasakian Einstein structures.

References in corpus (6)

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Cited by in corpus (4)

• Local classification and examples of an important class of paracontact metric manifolds
• Conformal Gauge Transformations in Thermodynamics
• Geometry of para-Sasakian metric as an almost conformal $\eta$-Ricci soliton
• On a remarkable class of paracontact metric manifolds