With the help of the zero-curvature equation and the super trace identity, we derive a super extensionof the Kaup-Newell hierarchy associated with a 3×3 matrix spectral problem and establish its super bi-Hamilton...With the help of the zero-curvature equation and the super trace identity, we derive a super extensionof the Kaup-Newell hierarchy associated with a 3×3 matrix spectral problem and establish its super bi-Hamiltonianstructures.Furthermore, infinite conservation laws of the super Kaup-Newell equation are obtained by using spectralparameter expansions.展开更多
We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negative...We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity.展开更多
The author considers the hyperbolic geometric flow introduced by Kong and Liu. Using the techniques and ideas to deal with the evolution equations along the Ricci flow by Brendle, the author derives the global forms...The author considers the hyperbolic geometric flow introduced by Kong and Liu. Using the techniques and ideas to deal with the evolution equations along the Ricci flow by Brendle, the author derives the global forms of evolution equations for Levi-Civita connection and curvature tensors under the hyperbolic geometric flow. In addition, similarly to the Ricci flow case, it is shown that any solution to tile hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.10871182 Innovation Scientists and Technicians Troop Construction Projects of Henan Province (084200410019)SRFDP (200804590008)
文摘With the help of the zero-curvature equation and the super trace identity, we derive a super extensionof the Kaup-Newell hierarchy associated with a 3×3 matrix spectral problem and establish its super bi-Hamiltonianstructures.Furthermore, infinite conservation laws of the super Kaup-Newell equation are obtained by using spectralparameter expansions.
文摘We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity.
文摘The author considers the hyperbolic geometric flow introduced by Kong and Liu. Using the techniques and ideas to deal with the evolution equations along the Ricci flow by Brendle, the author derives the global forms of evolution equations for Levi-Civita connection and curvature tensors under the hyperbolic geometric flow. In addition, similarly to the Ricci flow case, it is shown that any solution to tile hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.
