منابع مشابه
L_1 operator and Gauss map of quadric surfaces
The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...
متن کاملGauss map computation for free-form surfaces
The Gauss map of a smooth doubly{curved surface characterizes the range of variation of the surface normal as an area on the unit sphere. An algorithm to approximate the Gauss map boundary to any desired accuracy is presented, in the context of a tensor{product polynomial surface patch, r(u;v) for (u; v) 2 0; 1 ] 0; 1 ]. Boundary segments of the Gauss map correspond to variations of the normal ...
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Based on the work of Pinkall, characterizations of spherical curves are given whose corresponding Hopf cylinders are isothermic surfaces in the threedimensional sphere. Comparing these characterizations with results of Langer and Singer about elastic spherical curves we determine all isothermic Willmore Hopf tori.
متن کاملSpecial Isothermic Surfaces and Solitons
We establish a correspondence between Darboux’s special isothermic surfaces of type (A, 0, C, D) and the solutions of the second order p.d.e. Φ∆Φ − |∇Φ| + Φ = s, s ∈ R. We then use the classical Darboux transformation for isothermic surfaces to construct a Bäcklund transformation for this equation and prove a superposition formula for its solutions. As an application we discuss 1 and 2-soliton ...
متن کاملThe Gauss Map for Surfaces : Part 2 . the Euclidean Case
We study smooth maps t: M -> Ci of a Riemann surface M into the Grassmannian Gi of oriented 2-planes in E2 ' ' and determine necessary and sufficient conditons on t in order that it be the Gauss map of a conformai immersion X: M -» E2 + '. We sometimes view / as an oriented riemannian vector bundle; it is a subbundle of Ej/'. the trivial bundle over M with fibre E2 + l. The necessary and suffic...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1988-0964868-7