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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

When are the tangent sphere bundles of a Riemannian manifold reducible?


Author: E. Boeckx
Journal: Trans. Amer. Math. Soc. 355 (2003), 2885-2903
MSC (2000): Primary 53B20, 53C12, 53C20
Published electronically: March 14, 2003
MathSciNet review: 1975404
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Abstract: We determine all Riemannian manifolds for which the tangent sphere bundles, equipped with the Sasaki metric, are local or global Riemannian product manifolds.


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Additional Information

E. Boeckx
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
Email: eric.boeckx@wis.kuleuven.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03289-6
PII: S 0002-9947(03)03289-6
Keywords: Tangent sphere bundle, Sasaki metric, reducibility, Clifford structures, foliations
Received by editor(s): November 11, 2002
Received by editor(s) in revised form: January 21, 2003
Published electronically: March 14, 2003
Article copyright: © Copyright 2003 American Mathematical Society