Flows

Will J. Merry
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Will J. Merry: ETH Zürich, Departement Mathematik

Chapter Chapter 9 in Lectures on Differential Geometry I, 2026, pp 75-83 from Springer

Abstract: Abstract In this chapter we make contact with the theory of ordinary differential equations. A vector field defines an ordinary differential equation on a manifold, and just as in the Euclidean case, solutions to this ordinary differential equation exist (at least for a short time) and are unique. As with the Implicit Function Theorem, the local version of this statement follows readily from the corresponding Euclidean statement, but the global version is deeper.

Date: 2026
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DOI: 10.1007/978-3-032-03733-6_9

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