Abstract
Proposition 27.3 and Eq. (11) in Chap. 27 show that conjugate points are related to the curvature tensor via Jacobi fields; this tensor largely defines the topology of the manifold χ via the characteristic classes. Therefore, the topology and conjugate points interact with each other rather intimately. We first illustrate this general remark in connection with the notion of a normal neighborhood.
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© 2001 Springer-Verlag Berlin Heidelberg
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Postnikov, M.M. (2001). Some Additional Theorems I. In: Geometry VI. Encyclopaedia of Mathematical Sciences, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04433-9_28
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DOI: https://doi.org/10.1007/978-3-662-04433-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07434-9
Online ISBN: 978-3-662-04433-9
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