Decomposition of Killing vector fields on tangent sphere bundles
Konno, Tatsuo
Tohoku Math. J. (2), Tome 52 (2000) no. 4, p. 349-366 / Harvested from Project Euclid
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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.
Publié le : 2000-05-14
Classification:  53C25,  53C07 
@article{1178207818,
     author = {Konno, Tatsuo},
     title = {Decomposition of Killing vector fields on tangent sphere bundles},
     journal = {Tohoku Math. J. (2)},
     volume = {52},
     number = {4},
     year = {2000},
     pages = { 349-366},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178207818}
}

Konno, Tatsuo. Decomposition of Killing vector fields on tangent sphere bundles. Tohoku Math. J. (2), Tome 52 (2000) no. 4, pp.  349-366. http://gdmltest.u-ga.fr/item/1178207818/