The Riemannian manifolds with boundary and large symmetry

2008/01/07 by Chen, Zhi, Shi, Yiqian, Xu, Bin
#53C99 #57S15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0801.0948

Abstract

Sixty years ago, S. B. Myers and N. E. Steenrod (\it Ann. of Math. \bf 40 (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. Recently A. V. Bagaev and N. I. Zhukova (\it Siberian Math. J. \bf 48 (2007), 579-592) proved the same result for a Riemannian orbifold. In this paper, we firstly show that the isometry group of a Riemannian manifold M with boundary has dimension at most 1/2 dim M (dim M-1). Then we completely classify such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension.

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