منابع مشابه
Isothermic Surfaces and Hopf Cylinders
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 کاملar X iv : d g - ga / 9 61 00 06 v 1 9 O ct 1 99 6 BONNET PAIRS AND ISOTHERMIC SURFACES
A classical question in surface theory is which data are sufficient to describe a surface in space up to rigid motions. Bonnet suggested that mean curvature and metric should suffice to determine the surface generically. The local theory was developed by Bonnet [6], Cartan [4] and Chern [5] who showed the existence of various 1-parameter families of Bonnet surfaces, i.e., surfaces with the same...
متن کاملSupplement on Curved flats in the space of point pairs and Isothermic surfaces: A Quaternionic Calculus
A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. This calculus is then used to discuss the relation between curved flats in the symmetric space of point pairs and Darboux and Christoffel pairs of isothermic surfaces. A new viewpoint on relations between surfaces of constant mean curvature in certain space forms is presented — in particular, a new form of Bryant...
متن کاملStationary Isothermic Surfaces and Uniformly Dense Domains
We establish a relationship between stationary isothermic surfaces and uniformly dense domains. A stationary isothermic surface is a level surface of temperature which does not evolve with time. A domain Ω in the Ndimensional Euclidean space RN is said to be uniformly dense in a surface Γ ⊂ RN of codimension 1 if, for every small r > 0, the volume of the intersection of Ω with a ball of radius ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 1998
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-98-09219-5