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81.
The theory of Ribaucour transformations for hypersurfaces in space forms is established. For any such hypersurface M, that admits orthonormal principal vector fields, it was shown the existence of a totally umbilic hypersurface locally associated to M by a Ribaucour transformation. A method of obtaining linear Weingarten surfaces in a three-dimensional space form is provided. By applying the theory, a new one-parameter family of complete constant mean curvature (cmc) surfaces in the unit sphere, locally associated to the flat torus, is obtained. The family contains a class of complete cmc cylinders in the sphere. In particular, one gets a family of complete minimal surfaces and minimal cylinders, locally associated to the Clifford torus.Mathematics Subject Classifications (2000): 53C20. 相似文献
82.
Bernardo Lafuerza-Guillén Donal O’regan Reza Saadati 《Proceedings Mathematical Sciences》2007,117(1):61-70
We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness
of a quotient. 相似文献
83.
We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space. 相似文献
84.
T. Domínguez Benavides 《Journal of Mathematical Analysis and Applications》2004,291(1):100-108
Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping. 相似文献
85.
Let SB(X,Y) be the set of the bounded sublinear operators from a Banach space X into a Banach lattice Y. Consider π2(X,Y) the set of 2-summing sublinear operators. We study in this paper a variation of Grothendieck's theorem in the sublinear operators case. We prove under some conditions that every operator in SB(C(K),H) is in π2(C(K),H) for any compact K and any Hilbert H. In the noncommutative case the problem is still open. 相似文献
86.
On Covariant Phase Space and the Variational Bicomplex 总被引:1,自引:0,他引:1
Enrique G. Reyes 《International Journal of Theoretical Physics》2004,43(5):1267-1286
The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation. 相似文献
87.
The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions under which a generalized concircular transformation of one Weyl space onto another induces a generalized transformation oil its subspaces. Finally, it is shown that any totally geodesic or totally umbilical hypersurface of a generalized concircularly flat Weyl space is also generalized concircularly flat. 相似文献
88.
Ghulam Mustafa 《数学研究及应用》2003,23(3):413-421
本文引入了一种满足更一般的收缩不等式的多重函数类,并证明了属于该类的可测多重函数对的一些随机重合点定理。 相似文献
89.
We prove that all invariant distances on the universal Teichmuller space agree and are determined by the Grunsky coefficients of the naturally related conformal maps. This fact yields various important consequences; in particular, we obtain solutions of certain well-known geometric problems in complex analysis and related fields. 相似文献
90.
K-强凸空间的一些性质 总被引:4,自引:0,他引:4
结合Banach空间的Drop性,利用K维体积给出了K—强凸空间的一个新的定义,同时也给出了K—强光滑空间定义的K维体积表示,然后利用单位圆的切片证明了K—强凸空间是自反空间,进而证明了K—强凸空间与K—强光滑空间是一对对偶空间.最后利用Drop性的切片描述证明了K—强凸空间具有Drop性. 相似文献