论文标题
在亚riemannian歧管的等距沉浸式上
On isometric immersions of sub-Riemannian manifolds
论文作者
论文摘要
我们研究了与分布的几个成对正交子空间的相互曲率相关的，在非独立分布上具有riemannian度量的riemannian歧管（即具有riemannian度量的歧管）的曲率不变剂，并证明了次生次级次级Manifold的几何学不平等现象。作为应用，证明了具有相互正交分布的亚曼膜的不等式，包括标量和相互曲率。对于紧凑型亚曼叶，获得的不平等是由已知积分公式支持的几乎产物歧管的支持。
We study curvature invariants of a sub-Riemannian manifold (i.e., a manifold with a Riemannian metric on a non-holonomic distribution) related to mutual curvature of several pairwise orthogonal subspaces of the distribution, and prove geometrical inequalities for a sub-Riemannian submanifold. As applications, inequalities are proved for submanifolds with mutually orthogonal distributions that include scalar and mutual curvature. For compact submanifolds, inequalities are obtained that are supported by known integral formulas for almost-product manifolds.
