Abstract
In the first two sections of this chapter we discuss the geometry of the tangent bundle and the tangent sphere bundle. In Section 3 we briefly present a more general construction on vector bundles and in Section 4 specialize to the case of the normal bundle of a submanifold. The formalism for the tangent bundle and the tangent sphere bundle is of sufficient importance to warrant its own development, rather than specializing from the vector bundle case. In Section 5 we discuss briefly a contact structure on the projectivized tangent bundle of the hyperbolic plane and the geodesic flow on this bundle rather than on the unit tangent bundle, which is its usual setting.
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© 2010 Springer Science+Business Media, LLC
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Blair, D.E. (2010). Tangent Bundles and Tangent Sphere Bundles. In: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics, vol 203. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-4959-3_9
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DOI: https://doi.org/10.1007/978-0-8176-4959-3_9
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Publisher Name: Birkhäuser, Boston
Print ISBN: 978-0-8176-4958-6
Online ISBN: 978-0-8176-4959-3
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