https://neckpinch.com/authors/valentyna-petrusenko/New arXiv papers by Valentyna Petrusenko, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2007.13832/arxiv:2007.13832Mon, 27 Jul 2020 00:00:00 GMTKaveh Eftekharinasab, Valentyna Petrusenko — We establish a framework, namely, nuclear bounded Fréchet 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.Ricci flowEinstein metrics