论文标题
子帝国大地测量学的legendre奇异
Legendre singularities of sub-Riemannian geodesics
论文作者
论文摘要
让$ m $成为带有riemannian度量的表面和$ um $ $ m $的单位切线捆绑包，$ m $，$ m $ $ $ $ $ $ d $。在本文中，在$ m $ $ m $的Legendre纤维化$ um $ um $ um $ $ $ $ $ $ $ $（UM，D）$下的完整本地分类。从$ UM $到Riemannian Geodesics上的另一种Legendre纤维，在$ M $上的legendre Geodesics的Legendre奇异性也被完全分类。 Legendre奇异性的二元性与摆运动有关。
Let $M$ be a surface with a Riemannian metric and $UM$ the unit tangent bundle over $M$ with the canonical contact sub-Riemannian structure $D$ on $UM$. In this paper, the complete local classification of singularities, under the Legendre fibration $UM$ over $M$, is given for sub-Riemannian geodesics of $(UM, D)$. Legendre singularities of sub-Riemannian geodesics are classified completely also for another Legendre fibration from $UM$ to the space of Riemannian geodesics on $M$. The duality on Legendre singularities is observed related to the pendulum motion.
