Abstract
In this chapter, we investigate systematically the relationships of some of the differential geometric notions for submanifolds and for submersions. These involve the covariant derivative, Hessian, and curvature. The determination of the Hessian can be applied to compare the Laplacian in both contexts, because we can define the Laplacian as the trace of the Hessian in the finite dimensional case. The connection with the definition in terms of the divergence of the gradient will be given in Chapter XV.
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© 1999 Springer Science+Business Media New York
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Lang, S. (1999). Immersions and Submersions. In: Fundamentals of Differential Geometry. Graduate Texts in Mathematics, vol 191. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0541-8_14
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DOI: https://doi.org/10.1007/978-1-4612-0541-8_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6810-9
Online ISBN: 978-1-4612-0541-8
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