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Bundles with
spherical Euler class
Luis Guijarro, Thomas Schick and Gerard Walschap |
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Vol. 207 (2002), No. 2, 377–392
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Abstract |
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In this note, we show that the holonomy group of a Riemannian connection on a k-dimensional Euclidean vector bundle is transitive on the unit sphere bundle whenever the Euler class χ is spherical. We extract several consequences from this, among them that this is always the case as long as χ does not vanish, and the base of the bundle is simply connected and rationally (k + 1)∕2-connected. |
Milestones
Published: 1 December 2002
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Authors |
| Luis Guijarro | |
| Departamento de Geometría y
Topología Universidad Complutense de Madrid Ciudad Universitaria s/n 28040 Madrid, Spain |
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| Thomas Schick | |
| FB Mathematik Uni. Goettingen Bunsenstrasse 3 37073 Goettingen Germany |
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| Gerard Walschap | |
| Department of Mathematics University of Oklahoma Norman OK 73019 |
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