Tohoku Mathematical Journal
2000
September
SECOND SERIES VOL. 52, NO. 3

Tohoku Math. J.
52 (2000), 349-366

Title DECOMPOSITION OF KILLING VECTOR FIELDS ON TANGENT SPHERE BUNDLES

Author Tatsuo Konno

(Received November 30, 1998, revised June 22, 1999)
Abstract. Given an orientable Riemannian manifold, we consider the bundle of oriented orthonormal frames and the tangent sphere bundle over it, which admit natural Riemannian metrics defined by the Riemannian connection. We show that there is a natural homomorphism between the Lie algebras of fiber preserving Killing vector fields on these bundles. In particular, for any orientable Riemannian manifold of dimension two, we show that the homomorphism is extended to an isomorphism between these Lie algebras.

1991 Mathematics Subject Classification. Primary 53C25; Secondary 53C07.

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