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arXiv · 2007.13832

Finslerian geodesics on Fr\'{e}chet manifolds

Kaveh Eftekharinasab·Valentyna Petrusenko
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Abstract

We establish a framework, namely, nuclear bounded Fr\'{e}chet manifolds endowed with Riemann-Finsler structures to study geodesic curves on certain infinite dimensional manifolds such as the manifold of Riemannian metrics on a closed manifold. We prove on these manifolds geodesics exist locally and they are length minimizing in a sense. Moreover, we show that a curve on these manifolds is geodesic if and only if it satisfies a collection of Euler-Lagrange equations. As an application, without much difficulty, we prove that the solution to the Ricci flow on an Einstein manifold is not geodesic.

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Kaveh Eftekharinasab, Valentyna Petrusenko. 2020-07-27. Finslerian geodesics on Fr\'{e}chet manifolds. https://doi.org/10.31926/but.mif.2020.13.62.1.11

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