The Degree of Symmetry of Certain Compact Smooth Manifolds II

Details The Degree of Symmetry of Certain Compact Smooth Manifolds II The Degree of Symmetry of Certain Compact Smooth Manifolds II

2005-05-30

arxiv.org/abs/math/0505646v2

Chin. Ann. Math. 28B(2), 2007, 195-204

Mathematics

Geometric Topology

11 pages, some misprints revised and some minor modifications to Remark 1.2 and Proof of Theorems 1.1 and 1.3 to make the pape

Scientific paper

10.1007/s11401-005-0578-x

In this paper, we give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain four dimensional fiber bundles by virtue of the rigidity theorem of harmonic maps 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 ${\Bbb C}P^2\times V$, where $V$ is closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.

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