Open AccessRiemannian cubics close to geodesics at the boundaries
Author(s) -
Margarida Camarinha,
F. Silva Leite,
P. E. Crouch
Publication year - 2022
Publication title -
journal of geometric mechanics
Language(s) - English
Resource type - Journals
eISSN - 1941-4897
pISSN - 1941-4889
DOI - 10.3934/jgm.2022003
Subject(s) - geodesic , exponential map (riemannian geometry) , boundary (topology) , mathematics , uniqueness , mathematical analysis , position (finance) , geodesic map , pure mathematics , geometry , scalar curvature , curvature , sectional curvature , finance , economics
In this paper we investigate the existence and uniqueness of Riemannian cubics under boundary conditions on position and velocity. We restrict the study to cubics close to geodesics at the boundaries. In other words, we consider the boundary data in a neighborhood of geodesic boundary data. We define a map that generalizes the Riemannian exponential, the biexponential. This map is used to establish the correspondence between initial and boundary data. We also emphasize the relation between biconjugate points and bi-Jacobi fields along cubics by means of the biexponential map.