共查询到20条相似文献,搜索用时 15 毫秒
1.
L. A. Masal’tsev 《Mathematical Notes》2000,67(2):176-182
A representation of the Joachimsthal surfaces (having a family of curvature lines that lie in totally geodesic 2-spheres)
in the sphereS
3 is obtained. It is proved that, if a surface of constant mean curvature inS
3 has one family of curvature lines lying in totally geodesic 2-spheres, then it is a surface of rotation.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 221–229, February, 2000. 相似文献
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Jayakumar Ramanathan 《manuscripta mathematica》1988,60(4):417-422
Isometric deformations of compact minimal surfaces in the standard three-sphere are studied. It is shown that a given surface admits only finitely many noncongruent minimal immersions intoS
3 with the same first fundamental form. 相似文献
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Miyuki Koiso 《manuscripta mathematica》1989,63(2):193-207
We give a sufficient condition on a Jordan curve in the 3-dimensional open hemisphereH ofS
3 in terms of the Hopf fibering under which spans a unique compact generalized minimal surface inH. The maximum principle for minimal surfaces inS
3 is proved and plays an important role in the proof of the uniqueness theorem.Dedicated to Professor Shingo Murakami on his 60th birthdayThis work was carried out while the author was a visitor to the Max-Planck-Institut für Mathematik. 相似文献
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Takahiro Miura 《Topology and its Applications》2012,159(3):623-632
Rudolph introduced the notion of braidzel surfaces as a generalization of pretzel surfaces, and Nakamura showed that any oriented link has a braidzel surface. In this paper, we introduce the notion of flat braidzel surfaces as a special kind of braidzel surfaces, and show that any oriented link has a flat braidzel surface. We also introduce and study a new integral invariant of links, named the flat braidzel genus, with respect to their flat braidzel surfaces. Moreover, we give a way to calculate the number of components, the distance from proper links, the Arf invariant, and a Seifert matrix of a given link through the flat braidzel notation. 相似文献
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Xiao-Song Lin 《Commentarii Mathematici Helvetici》1991,66(1):333-339
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LetM be a compact minimal surface inS
3. Y. J. Hsu[5] proved that if S222, thenM is either the equatorial sphere or the Clifford torus, whereS is the square of the length of the second fundamental form ofM, ·2 denotes theL
2-norm onM. In this paper, we generalize Hsu's result to any compact surfaces inS
3 with constant mean curvature.Supported by NSFH. 相似文献
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Manuel Ritoré Antonio Ros 《Transactions of the American Mathematical Society》1996,348(1):391-410
It is proved that the spaces of index one minimal surfaces and stable constant mean curvature surfaces with genus greater than one in (non fixed) flat three manifolds are compact in a strong sense: given a sequence of any of the above surfaces we can extract a convergent subsequence of both the surfaces and the ambient manifolds in the topology. These limits preserve the topological type of the surfaces and the affine diffeomorphism class of the ambient manifolds. Some applications to the isoperimetric problem are given.
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Rodrigo Treviño 《Geometric And Functional Analysis》2014,24(1):360-386
We prove some ergodic theorems for flat surfaces of finite area. The first result concerns such surfaces whose Teichmüller orbits are recurrent to a compact set of ${SL(2,\mathbb{R})/SL(S,\alpha)}$ , where SL(S,α) is the Veech group of the surface. In this setting, this means that the translation flow on a flat surface can be renormalized through its Veech group. This result applies in particular to flat surfaces of infinite genus and finite area. Our second result is an criterion for ergodicity based on the control of deforming metric of a flat surface. Applied to translation flows on compact surfaces, it improves and generalizes a theorem of Cheung and Eskin et al. (Partially hyperbolic dynamics, laminations, and Teichmüller flow, Fields Inst. Commun., Vol. 51. Amer. Math. Soc., Providence, pp. 213–221, 2007). 相似文献
14.
Zong Liang Sun 《数学学报(英文版)》2014,30(11):1827-1832
By explicit constructions,we give direct proofs of the following results: for any distinct homotopy classes of simple closed curves α and β in a closed surface of genus g 1,there exist a hyperbolic structure X and a holomorphic quadratic differential q on X such that lX(α) = lX(β),extX(α) = extX(β) and lq(α) = lq(β),where lX(·),extX(·) and lq(·) are the hyperbolic length,the extremal length and the quadratic differential length respectively.These imply that there are no equivalent simple closed curves in hyperbolic surfaces or in flat surfaces. 相似文献
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Science China Mathematics - The aim of this paper is to verify that the study of generic conformally flat hypersurfaces in 4-dimensional space forms is reduced to a surface theory in the standard... 相似文献
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Yue Zhao 《Graphs and Combinatorics》1993,9(2-4):391-395
In this paper, we proved that ifG is a 3-connected graph of minimum valency δ = 6χ + 5 with α a non-negative integer and if there exists an embedding ψ ofG on a surface Σ of characteristic ?(Σ) = — α|V(G)∣+ β with the representativity of the embedding ψ ≥ 3, where ψ ε 0,1, thenG is edge reconstructible. 相似文献
19.
In this paper we study a sub-class of compact Ricci flat manifolds from certain standard constructions.
Research supported in part by NSF grant #DMS84-09447 and ONR contract #N-00014-85-K-0367. 相似文献
20.
Thomas Binder 《Journal of Geometry》2004,79(1-2):31-45
We study non-degenerate affine surfaces in A3 with a projectively
flat induced connection. The curvature of the affine metric
, the affine
mean curvature H, and the Pick invariant
J are related by
.
Depending on the rank of the span of the gradients of these functions,
a local classification of three groups is given.
The main result is the characterization of the projectively flat but
not locally symmetric surfaces as a solution of a system of ODEs.
In the final part, we classify projectively flat and
locally symmetric affine translation surfaces. 相似文献