共查询到20条相似文献,搜索用时 10 毫秒
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A translation surface in Euclidean space is a surface that is the sum of two regular curves \(\alpha \) and \(\beta \). In this paper we characterize all minimal translation surfaces. In the case that \(\alpha \) and \(\beta \) are non-planar curves, we prove that the curvature \(\kappa \) and the torsion \(\tau \) of both curves must satisfy the equation \(\kappa ^2 \tau = C\) where C is constant. We show that, up to a rigid motion and a dilation in the Euclidean space and, up to reparametrizations of the curves generating the surfaces, all minimal translation surfaces are described by two real parameters \(a,b\in \mathbb {R}\) where the surface is of the form \(\phi (s,t)=\beta _{a,b}(s)+\beta _{a,b}(t)\). 相似文献
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本文考虑欧氏空间中具有共形Gauss映照的曲面.从Gauss映照的观点给出了 veronese曲面的一个新特征. 相似文献
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本文借助于正交张量特征值的特性,采用剖分的方法.利用二维正交张量典则表示,很快就构造出一般n维欧氏空间上的正交张量的典则表示.利用Cayley-Hamilton定理,求得了正交张量各主不变量之间的相关方程,从而使得正交张量特征根的求解只需要在一个阶数不大于空间维数n的一半的代数方程上进行.本文还给出了正交张量的独立参数个数——自由度的计算公式. 相似文献
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In this paper we study general rotational surfaces in ${\mathbb{E}^4}$ whose meridian curves lie in two-dimensional planes. We firstly find all minimal general rotational surfaces by solving the differential equation that characterizes minimal general rotational surfaces. Then we determine all pseudo-umbilical general rotational surfaces in ${\mathbb{E}^4}$ . 相似文献
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Zu Huan YU Qing Zhong LI 《数学学报(英文版)》2007,23(11):2079-2086
In this note, a construction of minimal surfaces in Euclidean 3-space is given. By using the product of Weierstrass data of two known minimal surfaces, one gets a new Weierstrass data and a corresponding minimal surface from the Weierstrass representation. 相似文献
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LiJunYANG XianWuZENG 《数学学报(英文版)》2003,19(4):739-744
Two characterizations for a local diffeomorphism of R^n to be global one are given in terms of associated Wazewski equations.The two characterizations could be useful for the investigation of the Jacobian conjecture. 相似文献
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We introduce the notion of (0,m)-Codazzi tensors relative to an affine connection which extends the well known concept for m = 2. On compact Riemannian surfaces of genus we determine the dimension of the R-vector space of traceless Codazzi tensors, which depends on m and only, additionally we extend these result for genus zero. We give some exemplary applications to submanifolds in affine and in Riemannian geometry and to Weyl geometries. 相似文献
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?smail G?k O. Zeki Okuyucu Ferda? Kahraman H. Hilmi Hacisaliho?lu 《Advances in Applied Clifford Algebras》2011,21(4):707-719
In this paper we give a new definition of harmonic curvature functions in terms of B
2 and we define a new kind of slant helix which we call quaternionic B
2–slant helix in 4–dimensional Euclidean space E
4 by using the new harmonic curvature functions. Also we define a vector field D which we call Darboux quaternion of the real quaternionic B
2–slant helix in 4–dimensional Euclidean space E
4 and we give a new characterization such as:
"a: I ì \mathbb R ? E4{``\alpha : I \subset {\mathbb R} \rightarrow E^4} is a quaternionic B
2–slant helix ${\Leftrightarrow H^\prime_2 -KH_{1} = 0"}${\Leftrightarrow H^\prime_2 -KH_{1} = 0"} where H
2, H
1 are harmonic curvature functions and K is the principal curvature function of the curve α. 相似文献
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Ronaldo F. de Lima 《Annals of Global Analysis and Geometry》2001,20(4):325-343
Maximum principles at infinity generalize Hopf's maximum principle for hypersurfaces with constant mean curvature in R
n
. We establish such a maximum principle for parabolic surfaces in R3 with nonzero constant mean curvature and bounded Gaussian curvature. 相似文献
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Toru Sasahara 《Archiv der Mathematik》2012,99(3):281-287
A submanifold is said to be tangentially biharmonic if the bitension field of the isometric immersion that defines the submanifold has vanishing tangential component. The purpose of this paper is to prove that a surface in Euclidean 3-space has tangentially biharmonic normal bundle if and only if it is either minimal, a part of a round sphere, or a part of a circular cylinder. 相似文献
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The isometries of the space of convex bodies of Ed with respectto the Hausdorff-metric are precisely the mappings of the formC i(C) + D where i is a rigid motion of Ed and D a fixed convexbody. 相似文献
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In this paper we study translation surfaces of some new types in 3-Minkowski space E13 and give some classifications of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions. 相似文献
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In this paper we study surfaces foliated by a uniparametric family of circles in the homogeneous space Sol3. We prove that there do not exist such surfaces with zero mean curvature or with zero Gaussian curvature. We extend this study considering surfaces foliated by geodesics, equidistant lines or horocycles in totally geodesic planes and we classify all such surfaces under the assumption of minimality or flatness. 相似文献
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Conformal Metrics on the Unit Ball in Euclidean Space 总被引:2,自引:0,他引:2
We study densities on the unit ball in euclidean space whichsatisfy a Harnack type inequality and a volume growth conditionfor the measure associated with . For these densities a geometrictheory can be developed which captures many features of thetheory of quasiconformal mappings. For example, we prove generalizationsof the Gehring-Hayman theorem, the radial limit theorem andfind analogues of compression and expansion phenomena on theboundary. 1991 Mathematics Subject Classification: 30C65. 相似文献