Comparison theorems and hypersurfaces
Comparison theorems and hypersurfaces
复制标题
比较定理和超曲面
DOI：
--
复制
发表时间：
1987
期刊：
影响因子：
--
通讯作者：
J. Eschenburg
中科院分区：
文献类型：
--
作者：
J. Eschenburg
我们比较了不同黎曼流形中平行超曲面族的第二种基本形式。这为黎曼几何中的距离和体积比较定理提供了新的证明。特别地，对于任意r，我们得到了到完全测地线子流形距离≤r的点集的体积的一个新结果。解析的前提是研究了Riccati型ODE，该ODE由平行超曲面族的第二种基本形式所满足。
We compare the second fundamental forms of a family of parallel hypersurfaces in different Riemannian manifolds. This leads to new proofs for the distance and volume comparison theorems in Riemannian geometry. In particular, we get a new result on the volume of the set of points with distance≤r from a totally geodesic submanifold, for any r. The analytic prerequisite is the investigation of the Riccati type ODE which is satisfied by the second fundamental form of a parallel hypersurface family.