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November 2018 Pseudo-Einstein unit tangent sphere bundles
Jong Taek Cho, Sun Hyang Chun
Hiroshima Math. J. 48(3): 413-427 (November 2018). DOI: 10.32917/hmj/1544238035

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

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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

Information

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

zbMATH: 07090123
MathSciNet: MR3885269
Digital Object Identifier: 10.32917/hmj/1544238035

Subjects:
Primary: 53C25
Secondary: 53C15, 53D10

Rights: Copyright © 2018 Hiroshima University, Mathematics Program

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Vol.48 • No. 3 • November 2018
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