Hiroshima Mathematical Journal

Pseudo-Einstein unit tangent sphere bundles

Jong Taek Cho and Sun Hyang Chun

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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
Received: 29 January 2018
Revised: 11 June 2018
First available in Project Euclid: 8 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1544238035

Digital Object Identifier
doi:10.32917/hmj/1544238035

Mathematical Reviews number (MathSciNet)
MR3885269

Zentralblatt MATH identifier
07090123

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D10: Contact manifolds, general

Keywords
pseudo-Einstein structure generalized Tanaka-Webster connection

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


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