Geodetické křivky v sub-Riemannovské geometrii

Abstract

This thesis investigates the fundamental ideas and comparative structure of Riemannian and sub- Riemannian geodesics, the curves that locally minimise length. Geodesics, as defined variationally and by the Levi-Civita connection, are the shortest and straightest paths in Riemannian geometry. By limiting motion to a particular distribution within the tangent bundle, sub-Riemannian geometry expands on these ideas and creates a more complex and diverse class of geodesics, including regular and singular types. A thorough classification of normal and abnormal geodesics can beachieved by the study’s emphasis on the Lagrangian framework for obtaining geodesic equations under non-holonomic constraints.This thesis investigates the fundamental ideas and comparative structure of Riemannian and sub- Riemannian geodesics, the curves that locally minimise length. Geodesics, as defined variationally and by the Levi-Civita connection, are the shortest and straightest paths in Riemannian geometry. By limiting motion to a particular distribution within the tangent bundle, sub-Riemannian geometry expands on these ideas and creates a more complex and diverse class of geodesics, including regular and singular types. A thorough classification of normal and abnormal geodesics can beachieved by the study’s emphasis on the Lagrangian framework for obtaining geodesic equations under non-holonomic constraints.