The Riemannian manifolds with boundary and large symmetry

Details The Riemannian manifolds with boundary and large symmetry The Riemannian manifolds with boundary and large symmetry

2008-01-07

arxiv.org/abs/0801.0948v3

Mathematics

Differential Geometry

The former paper has been replaced by a substantially revised version. Title also changed

Scientific paper

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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