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Geodesics and Killing vector fields on the tangent sphere bundle

Published online by Cambridge University Press:  22 January 2016

Tatsuo Konno  and
Shukichi Tanno
Tatsuo Konno
Affiliation:
Mathematical Institute, Tôhoku University, Aoba-ku Sendai 980-8578, Japan, 94m05@math.tohoku.ac.jp
Shukichi Tanno
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Meguro-ku Tokyo 152-8551, Japan
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Abstract.

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We show that any Killing vector field on the unit tangent sphere bundle with Sasaki metric of a space of constant curvature k ≠ 1 is fiber preserving by studying some property of geodesies on the bundle. As a consequence, any Killing vector field on the unit tangent sphere bundle of a space of constant curvature k ≠ 1 can be extended to a Killing vector field on the tangent bundle.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 151 , September 1998 , pp. 91 - 97
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

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