共查询到20条相似文献,搜索用时 44 毫秒
1.
H. Hagen 《Monatshefte für Mathematik》1985,99(1):29-36
In this paper we investigate (k+1)-dimensional generalized ruled surfaces generated by a oneparameter family ofk-dimensional linear subspaces of then-dimensional Euclidean spaceE. Minding-isometries of ruled surfaces are special isometries, which let the generating space invariant. Some new results will be given, concerned with Mindingisometries of generalized ruled surfaces of arbitrary codimension. In this investigations quadratic hypersurfaces in the normal spaces are of great importance. 相似文献
2.
In this paper we study some mappings of skew ruled surfaces in simply isotropic space which preserve the generators. We study isometries, conformal mappings and mappings which preserve the area. Furthermore, we study mappings of surfaces in I
3
1 which preserve the asymptotic lines.Received December 18, 2001; in revised form July 12, 2002
Published online April 4, 2003 相似文献
3.
Among the eight geometries of Thurston, Sol3 is the space with the smallest number of isometries, for example, there are no rotations. In this work, we classify all surfaces with constant mean curvature that either are invariant by a 1-parameter group of isometries or are the product of two planar curves. 相似文献
4.
Dr. Georg Kronhuber 《Monatshefte für Mathematik》1975,80(4):283-296
Special theories exist for ruled surfaces in euclidean and affine spaces, which are fitted to the peculiarities of those surfaces. This paper deals with ruled surfaces in the 3-dimensional centro-affine space. The first part contains a theory about cones, which is needed subsequently. 相似文献
5.
This paper presents a method for kinematic generation of free-form ruled surfaces. The method is based on the kinematic displacement of lines. The ruled surfaces are represented as curves on a dual unit sphere. The curves are created by using the Lie Group structure of the dual space to generate dual displacement matrices for the lines. Free-form surfaces are created by repeated geodesic interpolation using the displacement matrices. An application for these surfaces is presented in five-axis cylindrical milling. 相似文献
6.
Günter Aumann 《manuscripta mathematica》1981,34(2-3):293-304
In this paper we investigate (k+1)-dimensional generalized ruled surfaces generated by a one-parameter family of k-dimensional linear subspaces of the n-dimensional Euclidean space En. All generalized ruled hypersurfaces (i. e. (n–1)-dimensional generalized ruled surfaces) with an everywhere vanishing mean curvature are listed. In other words, a complete characterization is given of all minimal ruled hypersurfaces. Moreover the principal curvatures of these surfaces are determined. 相似文献
7.
本文利用几何直纹面及曲线上秩-2局部自由层的一些性质,讨论射影空间中的直纹面一些特性,给出了非正则直纹面次数的下界并讨论了个维射影空间中次数接近下界的非正则直纹面的结构,如奇点集的结构,底曲线的结构及纤维束次数等,完全确定了这类曲面的几何结构。 相似文献
8.
Željka Milin Šipuš 《Periodica Mathematica Hungarica》2008,56(2):213-225
In this paper we study ruled Weingarten surfaces in the Galilean space. Weingarten surfaces are surfaces having a nontrivial
funcional relation between their Gaussian and mean curvature. We describe some further examples of Weingarten surfaces.
相似文献
9.
Marian Ioan Munteanu 《Mathematische Nachrichten》2014,287(8-9):1013-1024
A surface in homogeneous space is said to be an invariant surface if it is invariant under some of the two 1‐parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classify invariant surfaces with constant mean curvature and constant Gaussian curvature. Also, we characterize invariant surfaces that satisfy a linear Weingarten relation. 相似文献
10.
We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former,
which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve in the 3-sphere
or a Legendrian curve in the anti-de Sitter 3-space. We describe ruled Lagrangian surfaces and characterize the cyclic and
ruled Lagrangian surfaces which are solutions to the self-similar equation of the Mean Curvature Flow. Finally, we give a
partial result in the case of Hamiltonian stationary cyclic surfaces. 相似文献
11.
Steven F. Bellenot 《Israel Journal of Mathematics》1986,56(1):89-96
Each separable Banach space has an equivalent norm whose only isometries are ± identity. An equivalent norm on a non-separable
Hilbert space is constructed so that its only isometries are ± identity. 相似文献
12.
P.T. Eendebak 《Differential Geometry and its Applications》2008,26(6):600-612
In this article we study real 2-dimensional surfaces in the Grassmannian of 2-planes in a 4-dimensional vector space. These surfaces occur naturally as the fibers of jet bundles of partial differential equations.On the Grassmannian there is an invariant conformal quadratic form and we will use the structure induced by this quadratic form to study the surfaces. We give a topological classification of compact hyperbolic surfaces similar to the classification by Gluck and Warner [Duke Math. J. 50 (1) (1983)] of compact elliptic surfaces. In contrast with elliptic surfaces there are several topological possibilities for hyperbolic surfaces. We make a calculation of the differential invariants under the action of the group of conformal isometries. Finally, we analyze a class of surfaces called geometrically flat and show that within this class there exist many examples of non-trivial compact surfaces. 相似文献
13.
The isometries with respect to the Hausdorff metric of spaces of compact or compact convex subsets of certain compact metric spaces are precisely the mappings generated by isometries of the underlying spaces. In particular this holds when the underlying space is a finite dimensional torus or a sphere in a finite dimensional strictly convex smooth normed space. 相似文献
14.
We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of self-adjoint semigroups of partial isometries. We obtain a general structure result showing that every self-adjoint semigroup of partial isometries consists of “generalized weighted composition” operators on a space of square-integrable Hilbert-space valued functions. If the semigroup is finitely generated then the underlying measure space is purely atomic, so that the semigroup is represented as “zero-unitary” matrices. The same is true if the semigroup contains a compact operator, in which case it is not even required that the semigroup be self-adjoint. 相似文献
15.
P. Koltsaki 《Results in Mathematics》1999,35(3-4):266-275
Let S be a rectilinear congruence in the real 3-dimensional Euclidean space. N.K.Stephanidis has introduced the third quadratic differential form III of S [6]. In [7] he has defined the III-main ruled surfaces of S. In this paper we define and study new classes of ruled surfaces in S. 相似文献
16.
Yi Fang 《Archiv der Mathematik》1999,72(6):473-480
17.
Irene I. Onnis 《Annali di Matematica Pura ed Applicata》2008,187(4):667-682
We classify the profile curves of all surfaces with constant mean curvature in the product space , which are invariant under the action of a 1-parameter subgroup of isometries.
The author was supported by INdAM (Italy) and Fapesp (Brazil). 相似文献
18.
19.
Yoshihiro Nakamura 《Integral Equations and Operator Theory》1993,17(3):373-403
The structure of isometries on a Hilbert space are well studied. In this paper we study contractions which are one-dimensional perturbations of isometries, in particular, perturbations of the shift operator onH
2. 相似文献
20.
该文得到了两个同类的E_((2))型空间单位球面间等距线性算子的表现定理,这是首次在非具体范数的情形下取得此类结果. 相似文献