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March 2017 Unit tangent sphere bundles with the Reeb flow invariant Ricci operator
Jong Taek Cho, Sun Hyang Chun
Kodai Math. J. 40(1): 102-116 (March 2017). DOI: 10.2996/kmj/1490083226

Abstract

In this paper, we study unit tangent sphere bundles T1M whose Ricci operator $\bar{S}$ is Reeb flow invariant, that is, Lξ$\bar{S}$ = 0. We prove that for a 3-dimensional Riemannian manifold M, T1M satisfies Lξ$\bar{S}$ = 0 if and only if M is of constant curvature 1. Also, we prove that for a 4-dimensional Riemannian manifold M, T1M satisfies Lξ $\bar{S}$ = 0 and ℓ$\bar{S}$ξ = 0 if and only if M is of constant curvature 1 or 2, where ℓ = $\bar{R}$(·,ξ)ξ is the characteristic Jacobi operator.

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Jong Taek Cho. Sun Hyang Chun. "Unit tangent sphere bundles with the Reeb flow invariant Ricci operator." Kodai Math. J. 40 (1) 102 - 116, March 2017. https://doi.org/10.2996/kmj/1490083226

Information

Published: March 2017
First available in Project Euclid: 21 March 2017

zbMATH: 1366.53031
MathSciNet: MR3626576
Digital Object Identifier: 10.2996/kmj/1490083226

Rights: Copyright © 2017 Tokyo Institute of Technology, Department of Mathematics

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Vol.40 • No. 1 • March 2017
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