Results 1 to 10 of about 201,245 (267)
COLORING CURVES ON SURFACES [PDF]
Forum of Mathematics, Sigma, 2018 We study the chromatic number of the curve graph of a surface. We show that the chromatic number grows like $k\log k$ for the graph of separating curves on a surface of Euler characteristic $-k$.
JONAH GASTER +2 more
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Flat Approximations of Surfaces Along Curves
Demonstratio Mathematica, 2015 We consider a developable surface tangent to a surface along a curve on the surface. We call it an osculating developable surface along the curve on the surface. We investigate the uniqueness and the singularities of such developable surfaces.
Izumiya Shyuichi, Otani Saki
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Curves on ruled surfaces under infinitesimal bending [PDF]
Bulletin of Natural Sciences Research, 2021 Infinitesimal bending of curves lying with a given precision on ruled surfaces in 3-dimensional Euclidean space is studied. In particular, the bending of curves on the cylinder, the hyperbolic paraboloid and the helicoid are considered and appropriate ...
Najdanović Marija +2 more
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Crystallography on curved surfaces [PDF]
Proceedings of the National Academy of Sciences, 2006 We study static and dynamical properties that distinguish 2D crystals constrained to lie on a curved substrate from their flat-space counterparts. A generic mechanism of dislocation unbinding in the presence of varying Gaussian curvature is presented in the context of a model surface amenable to full analytical treatment.
Vitelli, Vincenzo +2 more
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Curves on K3 surfaces in divisibility 2
Forum of Mathematics, Sigma, 2021 We prove a conjecture of Maulik, Pandharipande and Thomas expressing the Gromov–Witten invariants of K3 surfaces for divisibility 2 curve classes in all genera in terms of weakly holomorphic quasi-modular forms of level 2.
Younghan Bae, Tim-Henrik Buelles
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Modeling Developable Surfaces using Quintic Bézier and Hermite Curves [PDF]
International Journal of Mathematical, Engineering and Management Sciences, 2023 The nature of the developable surfaces has similarities to the industrial materials that are not amenable to stretching. Regarding the benefit, the developable surfaces are widely used to model plat-metal-based industry products such as automobiles, ship
Kusno
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Curves on surfaces and surgeries
European Journal of Combinatorics, 2021 We study collections of curves in generic position on a closed surface whose complement consists of one disk only, up to orientation-preserving homeomorphism of the surface. We define a surgery operation on the set of such collections and prove that any two of them can be connected by a sequence of such surgeries.
Sane, Abdoul Karim, Sane, Abdoul
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Curves on Non-Orientable Surfaces and Crosscap Transpositions
Mathematics, 2022 Let Ng,n be a non-orientable surface of genus g with n punctures and one boundary component. In this paper, we describe multicurves in Ng,n making use of generalized Dynnikov coordinates, and give explicit formulae for the action of crosscap ...
S. Öykü Yurttaş
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Osculating surfaces of curves on surfaces
Lietuvos Matematikos Rinkinys, 2020 Oosculating sphere have been studied in classical differential geometry [1]. In this article the osculating surfaces of higher order of space curves on surfaces in Euclidean space is considered.
Kazimieras Navickis
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Curve Space: Classifying Curves On Surfaces [PDF]
Communications in Information and Systems, 2007 We design signatures for curves defined on genus zero surfaces. The signature classifies curves according to the conformal geometry of the given curves and their embedded surface. Based on Teichmuller theory, our signature describes not only the curve shape but also the intrinsic relationship between the curve and its embedded surface. Furthermore, the
Xianfeng Gu, Xin Li 0003, Hong Qin 0001
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