共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
Bang‐Yen Chen 《Mathematische Nachrichten》2005,278(11):1242-1281
A Lagrangian submanifold is called Maslovian if its mean curvature vector H is nowhere zero and its Maslov vector field JH is a principal direction of AH . In this article we classify Maslovian Lagrangian surfaces of constant curvature in complex projective plane CP 2 as well as in complex hyperbolic plane CH 2. We prove that there exist 14 families of Maslovian Lagrangian surfaces of constant curvature in CP 2 and 41 families in CH 2. All of the Lagrangian surfaces of constant curvature obtained from these families admit a unit length Killing vector field whose integral curves are geodesics of the Lagrangian surfaces. Conversely, locally (in a neighborhood of each point belonging to an open dense subset) every Maslovian Lagrangian surface of constant curvature in CP 2 or in CH 2 is a surface obtained from these 55 families. As an immediate by‐product, we provide new methods to construct explicitly many new examples of Lagrangian surfaces of constant curvature in complex projective and complex hyperbolic planes which admit a unit length Killing vector field. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
John A. Velling 《Journal of Geometric Analysis》1999,9(3):457-489
A set of conditions are given, each equivalent to the constancy of mean curvature of a surface in
H
3.It is shown that analogs of these equivalences exist for surfaces in
S
∞
2
,the bounding ideal sphere of
H
3,leading to a notion of constant mean curvature at infinity of
H
3.A parametrization of all complete constant mean curvature surfaces at infinity of
H
3
is given by holomorphic quadratic differentials on Ĉ,C, and
D. 相似文献
4.
Gabriel Ruiz-Hernández 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2011,81(1):55-67
An immersed surface M in N
n
×ℝ is a helix if its tangent planes make constant angle with ∂
t
. We prove that a minimal helix surface M, of arbitrary codimension is flat. If the codimension is one, it is totally geodesic. If the sectional curvature of N is positive, a minimal helix surfaces in N
n
×ℝ is not necessarily totally geodesic. When the sectional curvature of N is nonpositive, then M is totally geodesic. In particular, minimal helix surfaces in Euclidean n-space are planes. We also investigate the case when M has parallel mean curvature vector: A complete helix surface with parallel mean curvature vector in Euclidean n-space is a plane or a cylinder of revolution. Finally, we use Eikonal f functions to construct locally any helix surface. In particular every minimal one can be constructed taking f with zero Hessian. 相似文献
5.
In this paper we investigate existence and uniqueness of radial graphs ofconstant mean curvature (cmc) with prescribed boundary. Our main resultestablishes the existence of a minimal radial anullus spanning two givenconvex curves in parallel planes of R3; we also obtain a variant ofa well-known result of James Serrin about the existence of radial cmc graphsover convex domains in the sphere. 相似文献
6.
We classify positively curved self-dual Einstein Hermitian orbifold metrics of Galicki – Lawson on the weighted projective
planes. We thus determine which of the 3-Sasakian S1-reductions of S11 possess canonical variation metrics of positive sectional curvature.
Mathematics Subject Classifications (2000): 53C21, 53C25, 53C26 相似文献
7.
In this paper we characterize the spacelike hyperplanes in the Lorentz–Minkowski space L
n
+1 as the only complete spacelike hypersurfaces with constant mean curvature which are bounded between two parallel spacelike
hyperplanes. In the same way, we prove that the only complete spacelike hypersurfaces with constant mean curvature in L
n
+1 which are bounded between two concentric hyperbolic spaces are the hyperbolic spaces. Finally, we obtain some a priori estimates
for the higher order mean curvatures, the scalar curvature and the Ricci curvature of a complete spacelike hypersurface in
L
n
+1 which is bounded by a hyperbolic space. Our results will be an application of a maximum principle due to Omori and Yau, and
of a generalization of it.
Received: 5 July 1999 相似文献
8.
Jaigyoung Choe 《Mathematische Annalen》2002,323(1):143-156
We study under what condition a constant mean curvature surface can be round: i) If the boundary of a compact immersed disk
type constant mean curvature surface in consists of lines of curvature and has less than 4 vertices with angle , then the surface is spherical; ii) A compact immersed disk type capillary surface with less than 4 vertices in a domain
of bounded by spheres or planes is spherical; iii) The mean curvature vector of a compact embedded capillary hypersurface of
with smooth boundary in an unbounded polyhedral domain with unbalanced boundary should point inward; iv) If the kth order () mean curvature of a compact immersed constant mean curvature hypersurface of without boundary is constant, then the hypersurface is a sphere.
Received: 3 October 2000 / Published online: 1 February 2002 相似文献
9.
Sungwook Lee 《Annals of Global Analysis and Geometry》2006,29(4):355-401
It is shown that timelike surfaces of constant mean curvature ± in anti-de Sitter 3-space ?3 1(?1) can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in ?SL2? via Bryant type representation formulae. These Bryant type representation formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson–Guichard correspondence, between timelike surfaces of constant mean curvature ± 1 and timelike minimal surfaces in Minkowski 3-space E 3 1. The hyperbolic Gauß map of timelike surfaces in ?3 1(?1), which is a close analogue of the classical Gauß map is considered. It is discussed that the hyperbolic Gauß map plays an important role in the study of timelike surfaces of constant mean curvature ± 1 in ?3 1(?1). In particular, the relationship between the Lorentz holomorphicity of the hyperbolic Gauß map and timelike surface of constant mean curvature ± 1 in ?3 1(?1) is studied. 相似文献
10.
The total curvature of a compact C∞-immersed surface in Euclidean 3-space
3 can be interpreted as the average number of critical points for a linear ‘height’ function. The Morse inequalities provide
an intrinsic topological lower bound for the total curvature and ‘tight’ surfaces, which realize equality, have been an active
topic of research. The objective of this paper is to describe the natural notion of total curvature for C∞-singular surfaces which fail to immerse on C∞-embedded closed curves, but which have a
C∞-globally defined unit normal (e.g. caustics, or critical images for mappings of 3-manifolds into Euclidean 3-space). For
such surfaces total curvature consists of a sum of two-dimensional and one-dimensional integrals, which have various lower
bounds. Large sets of LT-surfaces which realize equality are then constructed. As an application, the orthogonal projection
of an immersed tight hypersurface in Euclidean 4-space is shown to have LT-tight critical image, and several related inequalities
are given.
Mathematics Subject Classifications (2000): 57N65, 14P99, 53C21, 53B25, 53B20. 相似文献
11.
Bang-Yen Chen 《Monatshefte für Mathematik》1980,90(3):185-194
A surfaceM in a Riemannian manifold is said to have parallel normalized mean curvature vector if the mean curvature vector is nonzero and the unit vector in the direction of the mean curvature vector is parallel in the normal bundle. In this paper, it is proved that every analytic surface in a euclideanm-spaceE
m
with parallel normalized mean curvature vector must either lies in aE
4 or lies in a hypersphere ofE
m
as a minimal surface. Moreover, it is proved that if a Riemann sphere inE
m
has parallel normalized mean curvature vector, then it lies either in aE
3 or in a hypersphere ofE
m
as a minimal surfaces. Applications to the classification of surfaces with constant Gauss curvature and with parallel normalized mean curvature vector are also given. 相似文献
12.
Rafael López 《Geometriae Dedicata》1999,76(1):81-95
We prove that a spacelike surface in L3 with nonzero constant mean curvature and foliated by pieces of circles in spacelike planes is a surface of revolution. When the planes containing the circles are timelike or null, examples of nonrotational constant mean curvature surfaces constructed by circles are presented. Finally, we prove that a nonzero constant mean curvature spacelike surface foliated by pieces of circles in parallel planes is a surface of revolution. 相似文献
13.
Rafael López 《Israel Journal of Mathematics》2008,167(1):283-301
A linear Weingarten surface in Euclidean space ℝ3 is a surface whose mean curvature H and Gaussian curvature K satisfy a relation of the form aH + bK = c, where a, b, c ∈ ℝ. Such a surface is said to be hyperbolic when a
2 + 4bc < 0. In this paper we study rotational linear Weingarten surfaces of hyperbolic type giving a classification under suitable
hypothesis. As a consequence, we obtain a family of complete hyperbolic linear Weingarten surfaces in ℝ3 that consists of surfaces with self-intersections whose generating curves are periodic.
Partially supported by MEC-FEDER grant no. MTM2007-61775. 相似文献
14.
Ulrich Pinkall 《manuscripta mathematica》1985,51(1-3):89-119
A hypersurface M in En is called a Dupin hypersurface if along each curvature surface of M the corresponding principal curvature is constant. For n=3 the only Dupin hypersurfaces are spheres, planes and the well known cyclides of Dupin. In this paper all Dupin hypersurfaces in E4 are explicitly determined. 相似文献
15.
Rafael López 《Annals of Global Analysis and Geometry》1997,15(3):201-210
In this paper we study constant mean curvature compact surfaces with two Jordan curves in parallel planes as boundary and we investigate the point at which the surface inherits the symmetries of its boundary. 相似文献
16.
Let be a hypersurface in the (m+1)-dimensional unit sphere Sm+1 without umbilics. Four basic invariants of x under the Möbius transformation group in Sm+1 are a Riemannian metric g called Möbius metric, a 1-form called Möbius form, a symmetric (0,2) tensor A called Blaschke tensor and symmetric (0,2) tensor B called Möbius second fundamental form. In this paper, we prove the following classification theorem: let be a hypersurface, which satisfies (i) 0, (ii) A+g+B0 for some functions and , then and must be constant, and x is Möbius equivalent to either (i) a hypersurface with constant mean curvature and scalar curvature in Sm+1; or (ii) the pre-image of a stereographic projection of a hypersurface with constant mean curvature and scalar curvature in the Euclidean space Rm+1; or (iii) the image of the standard conformal map of a hypersurface with constant mean curvature and scalar curvature in the (m+1)-dimensional hyperbolic space Hm+1. This result shows that one can use Möbius differential geometry to unify the three different classes of hypersurface with constant mean curvature and scalar curvature in Sm+1, Rm+1 and Hm+1.Partially supported the Alexander Humboldt Stiftung and Zhongdian grant of NSFC.Partially supported by RFDP, Qiushi Award, 973 Project and Jiechu grant of NSFC.Mathematics Subject Classification (2000):Primary 53A30; Secondary 53B25 相似文献
17.
Gabriele Anzellotti 《Annali di Matematica Pura ed Applicata》1979,119(1):297-316
Summary In this paper we prove a Harnack type inequality for non-negative solutions and supersolutions of second order quasilinear
elliptic equations on hypersurfaces (inR
n) of Lp prescribed mean curvature, with p>n. In the last section an application to non-parametric surfaces of Lipschitz mean curvature
is given.
Entrata in Redazione il 13 giugno 1977. 相似文献
Entrata in Redazione il 13 giugno 1977. 相似文献
18.
Paweł Strzelecki Heiko von der Mosel 《Calculus of Variations and Partial Differential Equations》2006,25(4):431-467
Motivated by previous work on elastic rods with self-contact, involving the concept of the global radius of curvature for
curves (as defined by Gonzalez and Maddocks), we define the global radius of curvature Δ[X] for a wide class of continuous parametric surfaces X for which the tangent plane exists on a dense set of parameters. It turns out that in this class of surfaces a positive lower
bound Δ[X] ≥ θ > 0 provides, naively speaking, the surface with a thickness of magnitude θ; it serves as an excluded volume constraint
for X, prevents self-intersections, and implies that the image of X is an embedded C1-manifold with a Lipschitz continuous normal. We also obtain a convergence and a compactness result for such thick surfaces,
and show one possible application to variational problems for embedded objects: the existence of ideal surfaces of fixed genus
in each isotopy class.
The proofs are based on a mixture of elementary topological, geometric and analytic arguments, combined with a notion of the
reach of a set, introduced by Federer in 1959.
Mathematics Subject Classification (2000) 49Q10, 53A05, 53C45, 57R52, 74K15 相似文献
19.
Yi Bing SHEN Xiao Hua ZHU 《数学学报(英文版)》2005,21(3):631-642
By using curvature estimates, we prove that a complete non-compact hypersurface M with constant mean curvature and finite L^n-norm curvature in R^1+1 must be minimal, so that M is a hyperplane if it is strongly stable. This is a generalization of the result on stable complete minimal hypersurfaces of R^n+1. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite L^1-norm curvature in R^1+1 are considered. 相似文献
20.
The role that a prescribed holomorphic Hopf (Quadratic) differential A(z) dz dz plays in the construction of a negatively
curved immersed simply connected complete surface ∑0
of prescribed constant mean curvature c ∈ (−1, 1)in the hyperbolic 3-Space
H
3
is investigated in this work. When a holomorphic function A(z), which is the coefficient function of the Hopf differential,
is prescribed on a unit disk |z| < 1,it is shown that the unit disk |z| < 1can be immersed in the hyperbolic 3-Space
H
3
as a negatively curved complete surface of constant mean curvature c ∈ (−1, 1),provided that |A(z)| satisfies a certain growth condition. Moreover, it is shown that the unit disk |z| < 1can be uniquely embedded in
H
3
when the holomorphic function A(z) has a certain admissible structure. 相似文献