首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
A triangulation of a closed surface is said to be d-covered if all of its edges are covered by vertices of degree d. We shall give constructive characterizations of 5- and 6-covered triangulations. Received: July 17, 1998?Final version received: January 12, 2000  相似文献   

2.
A triangulation on a closed surface is said to be d-covered if each of its edges is covered by a vertex of degree d. We shall give some infinite series of d-covered triangulations on each closed surface of non-positive (respectively positive) Euler characteristic for 5d12 (respectively 10).Final version received: April 25, 2003  相似文献   

3.
A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly non-orientable) surface of genus g ≥ 0 with b ≥ 0 boundary components is O(g + b). So far, the result was known only for surfaces without boundary (b = 0). While our technique yields a worse constant in the O(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary.  相似文献   

4.
5.
Siberian Mathematical Journal - The degree $ d(x) $ of a vertex or face $ x $ in a graph $ G $ on the plane or other orientable surface is the number of incident edges. A face $ f=v_{1}ldots...  相似文献   

6.
7.
In this paper, we study the moduli spaces of flat surfaces with cone singularities verifying the following property: there exists a union of disjoint geodesic tree on the surface such that the complement is a translation surface. Those spaces can be viewed as deformations of the moduli spaces of translation surfaces in the space of flat surfaces. We prove that such spaces are quotients of flat complex affine manifolds by a group acting properly discontinuously, and preserving a parallel volume form. Translation surfaces can be considered as a special case of flat surfaces with erasing forest, in this case, it turns out that our volume form coincides with the usual volume form (which are defined via the period mapping) up to a multiplicative constant. We also prove similar results for the moduli space of flat metric structures on the n-punctured sphere with prescribed cone angles up to homothety. When all the angles are smaller than 2π, it is known (cf. [T]) that this moduli space is a complex hyperbolic orbifold. In this particular case, we prove that our volume form induces a volume form which is equal to the complex hyperbolic volume form up to a multiplicative constant.  相似文献   

8.
We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used The authors acknowledge the support of the Australian Research Council  相似文献   

9.
Journal of Applied and Industrial Mathematics - The distinguishing number (index) $$D(G)$$ ( $$D^{\prime }(G) $$ ) of a graph $$G $$ is the least integer $$d $$ such that $$G $$ has a vertex...  相似文献   

10.
We investigate closed surfaces in Euclidean 3-space satisfying certain functional relations κ = F(λ) between the principal curvatures κ, λ. In particular we find analytic closed surfaces of genus zero where F is a quadratic polynomial or F(λ) = cλ2n+1. This generalizes results by H. Hopf on the case where F is linear and the case of ellipsoids of revolution where F(λ) = cλ3.  相似文献   

11.
We investigate closed surfaces in Euclidean 3-space satisfying certain functional relations κ = F(λ) between the principal curvatures κ, λ. In particular we find analytic closed surfaces of genus zero where F is a quadratic polynomial or F(λ) = cλ2n+1. This generalizes results by H. Hopf on the case where F is linear and the case of ellipsoids of revolution where F(λ) = cλ3.  相似文献   

12.
13.
Bihermitian Structures on Complex Surfaces   总被引:2,自引:0,他引:2  
Bihermitian complex surfaces are oriented conformal four-manifoldsadmitting two independent compatible complex structures. Non-anti-self-dualbihermitian structures on R4 and the four-dimensional torusT4 have recently been discovered by P. Kobak. We show that anoriented compact 4-manifold, admitting a non-anti-self-dualbihermitian structure, is a torus or K3 surface in the stronglybihermitian case (when the two complex structures are independentat each point) or, otherwise, must be obtained from the complexprojective plane or a minimal ruled surface of genus less than2 by blowing up points along some anti-canonical divisor (butthe actual existence of bihermitian structures in the lattercase is still an open question). The paper includes a generalmethod for constructing non-anti-self-dual bihermitian structureson tori, K3 surfaces and S1 x S3. Further properties of compactbihermitian surfaces are also investigated. 1991 MathematicsSubject Classification: 53C12, 53C55, 32J15.  相似文献   

14.
It is known that for any closed surface F2, every even embedding on F2 with sufficiently large representativity is 4-colorable. In this paper, we shall characterize 3-colorable even embeddings on F2 with sufficiently large representativity.  相似文献   

15.
For the classes of the mappings Lipschitz in the sub-Riemannian sense and taking values in the Heisenberg group we introduce some suitable notions of variation of an argument and the corresponding increment of the area functional and derive several basic properties of maximal surfaces on the five-dimensional sub-Lorentzian structures.  相似文献   

16.
Streets and Tian introduced a parabolic flow of pluriclosed metrics. We classify the long time behavior of homogeneous solutions of this flow on closed complex surfaces including minimal Hopf, Inoue, Kodaira, and non-Kähler, properly elliptic surfaces. We also construct expanding soliton solutions to the flow on the universal covers of these surfaces by taking blowdown limits of these homogeneous solutions.  相似文献   

17.
We consider triangulations of surfaces with boundary and marked points. These triangulations are classified with respect to flip equivalence. The results obtained are applied to the homotopy classification of functions without critical points on 2-manifolds. It is shown that the set of such functions satisfies the one-parametric h-principle.  相似文献   

18.
In this note, we show that given a closed, orientable genus-g surface S g , any hyperbolic toral automorphism has a positive power which induces a quadratic, orientable pseudo-Anosov homeomorphism on S g . To show this, we lift Anosov toral automorphisms through a ramified topological covering and present the lifted homeomorphism via a standard set of Lickorish twists. This construction provides a general method of producing pseudo-Anosov maps of closed surfaces with predetermined orientable foliations and quadratic dilatation. Since these lifted automorphisms have orientable foliations, this construction is a sort of converse to that of Franks and Rykken [Trans. Amer. Math. Soc. 1999], who established that one can associate to a quadratic pseudo-Anosov homeomorphism with oriented unstable foliation a hyperbolic toral automorphism.  相似文献   

19.
The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Civita connection. In this article, we prove that an analogue of the uniformization theorem also holds for connections with metric torsion in the case of non-positive Euler characteristic. Our main tool is an adapted form of the Ricci flow.  相似文献   

20.
We introduce orbifold Euler numbers for normal surfaces withboundary Q-divisors. These numbers behave multiplicatively underfinite maps and in the log canonical case we prove that theysatisfy the Bogomolov–Miyaoka–Yau type inequality.Existence of such a generalization was earlier conjectured byG. Megyesi [Proc. London Math. Soc. (3) 78 (1999) 241–282].Most of the paper is devoted to properties of local orbifoldEuler numbers and to their computation. As a first application we show that our results imply a generalizedversion of R. Holzapfel's ‘proportionality theorem’[Ball and surface arithmetics, Aspects of Mathematics E29 (Vieweg,Braunschweig, 1998)]. Then we show a simple proof of a necessarycondition for the logarithmic comparison theorem which recoversan earlier result by F. Calderón-Moreno, F. Castro-Jiménez,D. Mond and L. Narváez-Macarro [Comment. Math. Helv.77 (2002) 24–38]. Then we prove effective versions of Bogomolov's result on boundednessof rational curves in some surfaces of general type (conjecturedby G. Tian [Springer Lecture Notes in Mathematics 1646 (1996)143–185)]. Finally, we give some applications to singularitiesof plane curves; for example, we improve F. Hirzebruch's boundon the maximal number of cusps of a plane curve. 2000 MathematicalSubject Classification: 14J17, 14J29, 14C17.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号