A first order prolongation of the conventional space
R. Ya. Matsyuk
TL;DR
This paper introduces a third-order variational equation in three-dimensional space that characterizes autoparallel curves of a certain connection, expanding the mathematical understanding of geometric structures.
Contribution
It presents a novel third-order variational equation for describing autoparallel curves, extending the classical theory of connections in differential geometry.
Findings
Derivation of a third-order variational equation
Application to autoparallel curves of a connection
New insights into geometric structures in 3D space
Abstract
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
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Taxonomy
TopicsNonlinear Waves and Solitons · Geometric Analysis and Curvature Flows · Differential Equations and Numerical Methods