搜索结果: 1-6 共查到“数理逻辑与数学基础 curvature”相关记录6条 . 查询时间(0.031 秒)
Positive scalar curvature, K-area and essentialness
Positive scalar curvature K-area essentialness
2010/11/23
The Lichnerowicz formula yields an index theoretic obstruction to positive scalar curvature metrics on closed spin manifolds. The most general form of this obstruction is due to Rosenberg and takes va...
Biharmonic submanifolds with parallel mean curvature vector field in spheres
Biharmonic submanifolds parallel mean curvature vector field
2010/11/12
We present some results on the boundedness of the mean curvature of proper biharmonic submanifolds in spheres. A partial classification result for proper biharmonic submanifolds with parallel mean cur...
On complete stable minimal surfaces in 4-manifolds with positive isotropic curvature
minimal surfaces 4-manifolds positive isotropic curvature
2010/11/12
We prove the nonexistence of stable immersed minimal surfaces uniformly conformally equivalent to the complex plane in any complete orientable four-dimensional Riemannian manifold with uniformly posi...
Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation
integrable Weingarten surfaces soliton theory equation possesses
2010/4/1
In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation wit...
Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere
principal curvature Clifford torus Gauss equations
2007/12/12
In this paper, we give a characterization of tori $S^1\left(\sqrt{\frac{nr+2-n}{nr}}\right)\times S^{n-1}\left(\sqrt{\frac{n-2}{nr}}\right)$ and $S^m\left(\sqrt{\frac{m}{n}}\right)\times S^{n-m}\left(...
Links between different analytic descriptions of constant mean curvature surfaces
mean curvature math
2010/11/1
Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system \[ \begin{split} &\partial \psi_{1...