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| The Degree of Symmetry of Certain Compact Smooth Manifolds II |
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Citation： |
Bin XU.The Degree of Symmetry of Certain Compact Smooth Manifolds II[J].Chinese Annals of Mathematics B,2007,28(2):195~204 |
| Page view： 992
Net amount： 794 |
Authors： |
Bin XU; |
Foundation： |
the Japanese Government Scholarship, the Japan Society for the Promotion of Science Postdoctoral Fellowship for Foreign Researchers, the Focused Research Group Postdoctoral Fellowship, the Program of Visiting Scholars at Chern Institute of Mathematics and the National Natural Science Foundation of China (No. 10601053). |
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| Abstract： |
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 ${\Bbb C}P^2\times V$, 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. |
Keywords： |
Degree of symmetry, Fiber bundle, Cobordism, Non-positive Curvature, Harmonic map, First cohomology |
Classification： |
57S15, 53C44 |
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