Abstract Conformal geodesics form an invariantly defined family of unparametrized curves in a conformal manifold generalizing unparametrized geodesics/paths of projective connections. The equation describing them is of third order, and it was an open problem whether they are given by an Euler–Lagrange…
Cham: Springer International Publishing, 2025-09-02
ABSTRACT The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well‐known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent…
Diese Dissertation untersucht die Struktur von Nijenhuis-Operatoren in Gegenwart eines Einheitsvektorfeldes sowie deren Verbindungen zu F-Mannigfaltigkeiten und Frobenius - Mannigfaltigkeiten. In dieser Arbeit stellen wir den Zerlegungssatz für Nijenhuis-Operatoren mit einem Einheitsvektorfeld auf und…
Given a smooth family of unparameterized curves such that through every point in every direction there passes exactly one curve, does there exist a Lagrangian with extremals being precisely this family? It is known that in dimension 2 the answer is positive. In dimension 3, it follows from the work of…
We show that geodesic random walks on a complete Finsler manifold of bounded geometry converge to a diffusion process which is, up to a drift, the Brownian motion corresponding to a Riemannian metric.
Two (pseudo-) Riemannian metrics are called projectively equivalent, if they possess the same geodesics (considered as unparametrized curves). C-projective eqivalence is a natural translation of projective equivalence to Kähler manifolds: A regular curve on a Kähler manifold (M, g, J) is called J-planar,…
In the literature different concepts of compatibility between a projective structure P \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr…
Two Finsler metrics on the same manifold are called projectively equivalent, if they have the same unparametrized, oriented geodesics. A vector field on the manifold is called projective for a Finsler metric, if its flow takes geodesics to geodesics as unparametrized curves. In this dissertation, after…