The Degree of Symmetry of Certain Compact Smooth Manifolds II*
The Degree of Symmetry of Certain Compact Smooth Manifolds II*
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DOI：
10.1007/s11401-005-0578-x
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发表时间：
2003-07
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影响因子：
--
通讯作者：
Bin Xu
中科院分区：
文献类型：
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作者：
Bin Xu
摘要：利用Schoen和Yau的调和映射刚性定理(Topology, 18, 1979, 361–380)，我们在共棱意义上给出了某些具有非平凡四维纤维的紧致纤维束的对称度和半简对称度的锐估计。作为该估计的推论，我们计算 ℂP2×V 的对称度和半简单对称度，其中 V 是一个封闭的光滑流形，允许非正曲率的实解析黎曼度量。此外，通过Albanese映射，我们得到了对其一维上同调有一定限制的紧致光滑流形对称度的锐估计。
AbstractWe 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, whereVis 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.