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81.
We give a necessary and sufficient condition for a submanifold with parallel focal structure to give rise to a global foliation of the ambient space by parallel and focal manifolds. We show that this is a singular Riemannian foliation with complete orthogonal transversals. For this object we construct an action on the transversals that generalizes the Weyl group action for polar actions.
82.
General boundary conditions (branes') for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morphisms and at the perturbative quantum level to the category of associative algebras (deforming algebras of functions on Poisson manifolds) with bimodules as morphisms. Possibly singular Poisson manifolds arising from reduction enter naturally into the picture and, in particular, the construction yields (under certain assumptions) their deformation quantization. 相似文献
83.
84.
§1.IntroductionLetNn+ppbean(n+p)-dimensionalconnectedpseudo-Riemannianmanifoldofindexp.IfNn+ppiscompleteandhasconstantsection... 相似文献
85.
86.
Danh Hua Quoc Nam Vo Van Au Nguyen Huy Tuan Donal O'Regan 《Mathematical Methods in the Applied Sciences》2019,42(18):6672-6685
In this paper, we consider the nonlinear biharmonic equation. The problem is ill‐posed in the sense of Hadamard. To obtain a stable numerical solution, we consider a regularization method. We show rigourously, with error estimates provided, that the corresponding regularized solutions converge to the true solution strongly in uniformly with respect to the space coordinate under some a priori assumptions on the solution. 相似文献
87.
研究了由三维Minkowski空间$E^3_1$中一个类空曲面$S_1$上一个单参数测地曲线族的切线所构成的直线汇$T$,它以$S_1$为一个焦曲面.证明了$T$的两个可展曲面族沿着第二个焦曲面$S_2$的正交曲线网相交的充要条件是$S_1$是可展曲面.对于$T$的两个焦曲面$S_1$和$S_2$之间沿着同一光线的对应,还证明了其保持渐近曲线网的充要条件.最后,研究了$T$的正交曲面$S$,并且证明了如果$S$是$E^3_1$中的一个极大曲面,那么,$T$的焦曲面$S_1$和$S_2$之间沿着同一光线的对 相似文献
88.
本文研究了S^(2+p)中2维子流形的莫比乌斯刚性问题.设M^(2)是^(2+p)维单位球S^(2+p)中的无脐子流形,M^(2)在S^(2+p)的莫比乌斯变换群下的四个莫比乌斯基本量为莫比乌斯度量g,Blaschke张量A,莫比乌斯形式Φ以及莫比乌斯第二基本形式B,利用不等式估计,证明了下列刚性定理:设x:M^(2)→S^(2+p)是^(2+p)维单位球S^(2+p)中莫比乌斯形式消失的2维紧致子流形,Blaschke张量A的行列式Det A=c(const)>0,若tr A≥1/4,那么x(M^(2))莫比乌斯等价于S^(2+p)中常曲率极小子流形或者S^(3)(1/√1+c^(2))中环面S^(1)(r)×S^(1)(√1/1+c^(2)-r^(2)),其中r^(2)=2-√1-64c/4(1+c^(2)).本文的证明补充了文献[3]中2维子流形情形. 相似文献
89.
In the biharmonic submanifolds theory there is a generalized Chen’s conjecture which states that biharmonic submanifolds in a Riemannian manifold with non-positive sectional curvature must be minimal. This conjecture turned out false by a counter example of Y.L. Ou and L. Tang in Ou and Tang (2012). However it remains interesting to find out sufficient conditions which guarantee this conjecture to be true. In this note we prove that:1. Any complete biharmonic submanifold (resp. hypersurface) in a Riemannian manifold with non-positive sectional curvature (resp. Ricci curvature) which satisfies an integral condition: for some , , where is the mean curvature vector field of , must be minimal. This generalizes the recent results due to N. Nakauchi and H. Urakawa in Nakauchi and Urakawa (2013, 2011).2. Any complete biharmonic submanifold (resp. hypersurface) in a Riemannian manifold of at most polynomial volume growth whose sectional curvature (resp. Ricci curvature) is non-positive must be minimal.3. Any complete biharmonic submanifold (resp. hypersurface) in a non-positively curved manifold whose sectional curvature (resp. Ricci curvature) is smaller than for some which satisfies that is of at most polynomial growth of , must be minimal.We also consider -superbiharmonic submanifolds defined recently in Wheeler (2013) by G. Wheeler and prove similar results for -superbiharmonic submanifolds, which generalize the result in Wheeler (2013). 相似文献
90.