Let M be a compact Kahler surface with positive scalar curvature, P(M, SU(N)) a principal fibre bundle. Then an irreducible Yang-Mills connection ▽ on P must be an antiself-dual connection, provided∫_M|Ф|~2【C.Here...Let M be a compact Kahler surface with positive scalar curvature, P(M, SU(N)) a principal fibre bundle. Then an irreducible Yang-Mills connection ▽ on P must be an antiself-dual connection, provided∫_M|Ф|~2【C.Here Ф is the projection of the curvature F of the connection ▽ on the Khler form of M, and C is an a-priori postive constant independent of connections on P.展开更多
In this article, we introduce the Hausdorff convergence to derive a differentiable sphere theorem which shows an interesting rigidity phenomenon on some kind of manifolds.
Using the theory of harmonic maps the authors discuss theproperties of the fundamental group of a complete nonpositivelycurved Riemannian manifold, and prove that the finitely generatedvirtual solvable subgroup of fun...Using the theory of harmonic maps the authors discuss theproperties of the fundamental group of a complete nonpositivelycurved Riemannian manifold, and prove that the finitely generatedvirtual solvable subgroup of fundamental group of a completenonpositively curved Riemannian manifold either is a peripheralsubgroup of fundamental group or can be realized by animmersed totall geodesic closed flat manifold. It generalizessome results of Gromoll-Wolf, Lawson-Yan and Schoen-Yau.展开更多
文摘Let M be a compact Kahler surface with positive scalar curvature, P(M, SU(N)) a principal fibre bundle. Then an irreducible Yang-Mills connection ▽ on P must be an antiself-dual connection, provided∫_M|Ф|~2【C.Here Ф is the projection of the curvature F of the connection ▽ on the Khler form of M, and C is an a-priori postive constant independent of connections on P.
基金Supported by the NNSF of China (10671066)the NSF of Shandong Province (Q2008A08)Scientific Research Foundation of QFNU
文摘In this article, we introduce the Hausdorff convergence to derive a differentiable sphere theorem which shows an interesting rigidity phenomenon on some kind of manifolds.
文摘Using the theory of harmonic maps the authors discuss theproperties of the fundamental group of a complete nonpositivelycurved Riemannian manifold, and prove that the finitely generatedvirtual solvable subgroup of fundamental group of a completenonpositively curved Riemannian manifold either is a peripheralsubgroup of fundamental group or can be realized by animmersed totall geodesic closed flat manifold. It generalizessome results of Gromoll-Wolf, Lawson-Yan and Schoen-Yau.
