Abstract
In the present paper, we study the pseudo-Hermitian almost CR structure of unit tangent sphere bundle $T_{1}M$ over a Riemannian manifold $M$. Then we prove that if the unit tangent sphere bundle $T_{1}M$ is pseudo-Einstein, that is, the pseudo- Hermitian Ricci tensor is proportional to the Levi form, then the base manifold $M$ is Einstein. Moreover, when $\dim M = 3$ or $4$, we prove that $T_{1}M$ is pseudo-Einstein if and only if $M$ is of constant curvature 1.
Citation
Jong Taek Cho. Sun Hyang Chun. "Pseudo-Einstein unit tangent sphere bundles." Hiroshima Math. J. 48 (3) 413 - 427, November 2018. https://doi.org/10.32917/hmj/1544238035
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