## Hiroshima Mathematical Journal

### Pseudo-Einstein unit tangent sphere bundles

#### 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.

#### Article information

Source
Hiroshima Math. J., Volume 48, Number 3 (2018), 413-427.

Dates
Revised: 11 June 2018
First available in Project Euclid: 8 December 2018

https://projecteuclid.org/euclid.hmj/1544238035

Digital Object Identifier
doi:10.32917/hmj/1544238035

Mathematical Reviews number (MathSciNet)
MR3885269

Zentralblatt MATH identifier
07090123

#### Citation

Taek Cho, Jong; Hyang Chun, Sun. Pseudo-Einstein unit tangent sphere bundles. Hiroshima Math. J. 48 (2018), no. 3, 413--427. doi:10.32917/hmj/1544238035. https://projecteuclid.org/euclid.hmj/1544238035