Year: 2024
Type: article
Abstract: We study the geometry of dynamic pairs (X, V) on a manifold M, where X is a vector field and V is a distribution on M, both satisfying a regularity condition. Special cases are pairs defined by systems of second order ODEs, geodesic sprays in Riemannian, Finslerian and Lagranian geometries, semi-Hamiltonian systems and control-affine systems. Analogs of conjugate points from the calculus of variations are defined for the pair (X, V). The main results give estimates for the position of conjugate points in terms of a curvature operator, analogously to the Cartan–Hadamard and Bonet–Myers theorems. Contrary to classical cases, no metric is given a priori, the distribution V may be nonintegrable and the curvature operator is defined in terms of (X, V).
DOI: 10.1051/cocv/2024079
Authors: B. Jakubczyk, W. Kryński
Institutions: Institute of Mathematics, Polish Academy of Sciences
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid:
Awards: G8982485600, G979321032
OpenAlex ID: W4404081835