共查询到20条相似文献,搜索用时 15 毫秒
1.
Sungwook Lee 《Differential Geometry and its Applications》2008,26(5):536-543
A generalized integral representation formula for spacelike maximal surfaces in a certain 3-dimensional homogeneous spacetime is obtained. This spacetime has a solvable Lie group structure with left invariant metric. The normal Gauß map of maximal surfaces in the homogeneous spacetime is discussed and the harmonicity of the normal Gauß map is studied. 相似文献
2.
Conformal geometry of surfaces in Lorentzian space forms 总被引:4,自引:0,他引:4
We study the conformal geometry of an oriented space-like surface in three-dimensional Lorentzian space forms. After introducing the conformal compactification of the Lorentzian space forms, we define the conformal Gauss map which is a conformally invariant two parameter family of oriented spheres. We use the area of the conformal Gauss map to define the Willmore functional and derive a Bernstein type theorem for parabolic Willmore surfaces. Finally, we study the stability of maximal surfaces for the Willmore functional.Dedicated to Professor T.J. WillmoreSupported by an FPPI Postdoctoral Grant from DGICYT Ministerio de Educación y Ciencia, Spain 1994 and by a DGICYT Grant No. PB94-0750-C02-02 相似文献
3.
Luis J. Alías Jorge H.S. de Lira Jorge A. Hinojosa 《Differential Geometry and its Applications》2012,30(1):1-12
We establish a spinorial representation for surfaces immersed with prescribed mean curvature in Heisenberg space. This permits to obtain minimal immersions starting with a harmonic Gauss map whose target is either the Poincaré disc or a hemisphere of the round sphere. 相似文献
4.
For spacelike stationary (i.e. zero mean curvature) surfaces in 4-dimensional Lorentz space, one can naturally introduce two Gauss maps and a Weierstrass-type representation. In this paper we investigate the global geometry of such surfaces systematically. The total Gaussian curvature is related with the surface topology as well as the indices of the so-called good singular ends by a Gauss–Bonnet type formula. On the other hand, as shown by a family of counterexamples to Osserman?s theorem, finite total curvature no longer implies that Gauss maps extend to the ends. Interesting examples include the deformations of the classical catenoid, the helicoid, the Enneper surface, and Jorge–Meeks? k-noids. Each family of these generalizations includes embedded examples in the 4-dimensional Lorentz space, showing a sharp contrast with the 3-dimensional case. 相似文献
5.
María A. León-Guzmán 《Differential Geometry and its Applications》2012,30(1):42-48
We prove that Lorentzian Hopf tori are the only immersed Lorentzian flat tori in a wide family of Lorentzian three-dimensional Killing submersions with periodic timelike orbits. 相似文献
6.
Jun-ichi Inoguchi 《Journal of Geometry》2005,82(1-2):83-90
Flat translation invariant surfaces in 3-dimensional Heisenberg group are classified. 相似文献
7.
In this work we prove the existence of totally geodesic two-dimensional foliation on the Lorentzian Heisenberg group H
3. We determine the Killing vector fields and the Lorentzian geodesics on H
3. 相似文献
8.
Luis J. Alías Marcos Dajczer Harold Rosenberg 《Calculus of Variations and Partial Differential Equations》2007,30(4):513-522
We study constant mean curvature graphs in the Riemannian three- dimensional Heisenberg spaces . Each such is the total space of a Riemannian submersion onto the Euclidean plane with geodesic fibers the orbits of a Killing field. We prove the existence and uniqueness of CMC graphs in with respect to the Riemannian submersion over certain domains taking on prescribed boundary values.
L. J. Alías was partially supported by MEC/FEDER project MTM2004-04934-C04-02 and Fundación Séneca project 00625/PI/04, Spain. 相似文献
9.
Xiang Ma 《manuscripta mathematica》2006,120(2):163-179
Using moving frame method, we study the Möbius geometry of a pair of conformally immersed surfaces in
. Two new invariants θ and ρ associated with them arise naturally as well as the notion of touch and co-touch. As an application, adjoint transform is defined for any Willmore surface in
. It always exists locally, hence generalizes known duality theorems of Willmore surfaces. Finally we characterize a pair of adjoint Willmore surfaces in terms of harmonic map. 相似文献
10.
We describe a new deformation that connects minimal disks with planar ends with minimal disks with helicoidal ends. In this way, we are able to construct a family of complete minimal surfaces with helicoidal ends that contains the singly periodic genus one helicoid of Hoffman, Karcher and Wei.Research of both authors was partially supported by MEC-FEDER grant number MTM2004-00160. 相似文献
11.
Hypersurfaces with constant scalar curvature in space forms 总被引:17,自引:0,他引:17
Li Haizhong 《Mathematische Annalen》1996,305(1):665-672
12.
It has been recently shown by Abresch and Rosenberg that a certain Hopf differential is holomorphic on every constant mean curvature surface in a Riemannian homogeneous 3-manifold with isometry group of dimension 4. In this paper we describe all the surfaces with holomorphic Hopf differential in the homogeneous 3-manifolds isometric to H2×R or having isometry group isomorphic either to the one of the universal cover of PSL(2,R), or to the one of a certain class of Berger spheres. It turns out that, except for the case of these Berger spheres, there exist some exceptional surfaces with holomorphic Hopf differential and non-constant mean curvature. 相似文献
13.
E.V. Petrov 《Differential Geometry and its Applications》2011,29(4):516-532
We obtain criteria for the harmonicity of the Gauss map of submanifolds in the Heisenberg group and consider the examples demonstrating the connection between the harmonicity of this map and the properties of the mean curvature field. Also, we introduce a natural class of cylindrical submanifolds and prove that a constant mean curvature hypersurface with harmonic Gauss map is cylindrical. 相似文献
14.
We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space R2,1. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group SU2 with SU1,1. The non-compactness of the latter group, however, means that the Iwasawa decomposition of the loop group, used to construct the surfaces, is not global. We prove that it is defined on an open dense subset, after doubling the size of the real form SU1,1, and prove several results concerning the behavior of the surface as the boundary of this open set is encountered. We then use the generalized Weierstrass representation to create and classify new examples of spacelike CMC surfaces in R2,1. In particular, we classify surfaces of revolution and surfaces with screw motion symmetry, as well as studying another class of surfaces for which the metric is rotationally invariant. 相似文献
15.
Oscar Perdomo 《Journal of Geometry》2006,84(1-2):100-105
In this paper we prove that if
is a closed minimal surface, then,
, for any homogeneous polynomial f of degree 3 with 0 a regular value of the function
. 相似文献
16.
17.
We study the mechanisms of the non properness of the action of
the group of diffeomorphisms on the space of Lorentzian metrics
of a compact manifold.
In particular, we prove that nonproperness entails the presence of
lightlike geodesic foliations of codimension 1.
On the 2-torus, we prove that a metric with constant curvature
along one of its lightlike foliation is actually flat. This
allows us to show that the restriction of the action to the set of
non-flat metrics is proper and that on the set of flat metrics of
volume 1 the action is ergodic.
Finally, we show that, contrarily to the Riemannian case, the
space of metrics without isometries is not always open. 相似文献
18.
F.E.C. Camargo R.M.B. Chaves L.A.M. Sousa Jr. 《Differential Geometry and its Applications》2008,26(6):592-599
In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space , n?3, with constant normalized scalar curvature R satisfying totally umbilical? 相似文献
19.
In this work we obtain a Simons' type inequality for a suitable tensor and apply it in order to obtain some results characterizing umbilical submanifolds and a product of submanifolds in a semi-Riemannian space form. 相似文献
20.