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| The Riemannian Manifolds with Boundary and Large Symmetry |
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Citation： |
Zhi CHEN,Yiqian SHI,Bin XU.The Riemannian Manifolds with Boundary and Large Symmetry[J].Chinese Annals of Mathematics B,2010,31(3):347~360 |
| Page view： 1800
Net amount： 1284 |
Authors： |
Zhi CHEN; Yiqian SHI; Bin XU; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10601053, 10671096,
10871184, 10971104). |
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| Abstract： |
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 dimM(dimM ?1). Then such Riemannian manifolds with boundary that |
Keywords： |
Riemannian manifold with boundary, Isometry, Rotationally symmetric
metric, Principal orbit |
Classification： |
53C99, 57S15 |
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