The degree of symmetry of certain compact smooth manifolds

Abstract

In this paper, we estimate the degree of symmetry and the semi-simple degree of symmetry of certain fiber bundles by virtue of the rigidity theorem with respect to the harmonic map due to Schoen and Yau. As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of certain product manifolds. In addition, by Albanese map, we estimate the degree of symmetry and the semi-simple degree of symmetry of a compact smooth manifold under some topological assumptions.