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November 2011 Infinitesimal isometries on tangent sphere bundles over three-dimensional manifolds
Tatsuo Konno
Hiroshima Math. J. 41(3): 343-366 (November 2011). DOI: 10.32917/hmj/1323700039

Abstract

In this article, we study the infinitesimal isometries on tangent sphere bundles over orientable three-dimensional Riemannian manifolds. Focusing on the vector fields which do not preserve fibers, we show the existence of lifts to the bundles of orthonormal frames. These lifts enable us to analyze the infinitesimal isometries by the symmetry of principal fiber bundles. We prove that the tangent sphere bundle admits a non-fiber-preserving infinitesimal isometry if and only if the base manifold has the same constant sectional curvatures as the fibers have. As an application, we classify the infinitesimal isometries on tangent sphere bundles for the three dimensional case.

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Tatsuo Konno. "Infinitesimal isometries on tangent sphere bundles over three-dimensional manifolds." Hiroshima Math. J. 41 (3) 343 - 366, November 2011. https://doi.org/10.32917/hmj/1323700039

Information

Published: November 2011
First available in Project Euclid: 12 December 2011

zbMATH: 1235.53051
MathSciNet: MR2895285
Digital Object Identifier: 10.32917/hmj/1323700039

Subjects:
Primary: 53C25
Secondary: 53C10

Rights: Copyright © 2011 Hiroshima University, Mathematics Program

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Vol.41 • No. 3 • November 2011
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