In this paper, we show that there exists no complete rotationally symmetric cusp metric on R^3. Also we consider the existence of the complete rotationally symmetric cusp metric with other situations.
Seventy years ago, Myers and Steenrod showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. In 2007, Bagaev and Zhukova proved the same result for a Riemannian orbifold...Seventy years ago, Myers and Steenrod showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. In 2007, Bagaev and Zhukova proved the same result for a Riemannian orbifold. In this paper, the authors first show that the isometry group of a Riemannian manifold M with boundary has dimension at most 1/2 dim M（dim M - 1）. Then such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension are completely classified.展开更多
文摘In this paper, we show that there exists no complete rotationally symmetric cusp metric on R^3. Also we consider the existence of the complete rotationally symmetric cusp metric with other situations.
基金Project supported by the National Natural Science Foundation of China (Nos. 10601053, 10671096,10871184, 10971104)Beijing International Mathematical Research Center for the hospitality and financial support during the course of this work
文摘Seventy years ago, Myers and Steenrod showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. In 2007, Bagaev and Zhukova proved the same result for a Riemannian orbifold. In this paper, the authors first show that the isometry group of a Riemannian manifold M with boundary has dimension at most 1/2 dim M（dim M - 1）. Then such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension are completely classified.
