The Riemannian Manifolds with Boundary and Large Symmetry
نویسندگان
چکیده
Sixty years ago, S. B. Myers and N. E. Steenrod (Ann. of Math. 40 (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a stru ture of Lie group. Re ently A. V. Bagaev and N. I. Zhukova (Siberian Math. J. 48 (2007), 579-592) proved the same result for a Riemannian orbifold. In this paper, we rstly 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 ompletely lassify su h Riemannian manifolds with boundary that their isometry groups attain the pre eding maximal dimension. Mathematics Subject Classification: Primary 53C99; Se ondary 57S15.
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