Para-Sasaki-like Riemannian manifolds and new Einstein metrics

Abstract

We extract a new class of paracontact paracomplex Riemannian manifolds arising from certain cone construction, call it para-Sasaki-like Riemannian manifold and give explicit examples. We define a hyperbolic extension of a paraholomorphic paracomplex Riemannian manifold, which is a local product of two Riemannian spaces with equal dimensions, showing that it is a para-Sasaki-like Riemannian manifold. If the starting paraholomorphic paracomplex Riemannian manifold is complete Einstein with negative scalar curvature then its hyperbolic extension is a complete Einstein para-Sasaki-like Riemannian manifold with negative scalar curvature thus producing new examples of complete Einstein Riemannian manifold with negative scalar curvature.

15 pages, v2: added completeness of the metric

References in corpus (1)

• Ricci-like solitons with vertical potential on Sasaki-like almost contact B-metric manifolds

Cited by in corpus (2)

• Para-Ricci-like Solitons on Almost Paracontact Almost Paracomplex Riemannian Manifolds
• Almost paracontact almost paracomplex Riemannian manifolds as extensions of 2-dimensional space-forms