Abstract
Throughout this chapter, by a manifold, we shall mean a C∞ manifold, for simplicity of language. Vector fields, forms and other objects will also be assumed to be C∞ unless otherwise specified. We let X be a manifold. We denote the R-vector space of vector fields by ΓT(X). Observe that ΓT(X) is also a module over the ring of functions \( \mathfrak{F} = \mathfrak{F}^\infty (X). \) We let π:TX →X be the natural map of the tangent bundle onto X.
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© 1995 Springer-Verlag New York, Inc.
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Lang, S. (1995). Covariant Derivatives and Geodesics. In: Lang, S. (eds) Differential and Riemannian Manifolds. Graduate Texts in Mathematics, vol 160. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4182-9_8
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DOI: https://doi.org/10.1007/978-1-4612-4182-9_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8688-2
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