The Riemannian manifolds with boundary and large symmetry

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 ½ dimM(dimM − 1). Then such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension are completely classified.

Keywords

Riemannian manifold with boundary / Isometry / Rotationally symmetric metric / Principal orbit

References

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