【摘 要】
：
We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional
【机 构】
：
Department of Mathematics,Chern Institute of Mathematics
【基金项目】
：
国家自然科学基金;the Program of Visiting Scholars at Chern Institute of Mathematics;the Focused Research Group Postdoctoral Fellowship;the Japanese Government Scholarship;the Japan Society for the Promotion o
论文部分内容阅读
We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2 × V, where V is a 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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