Surfaces containing two circles through each point
نویسندگان
چکیده
منابع مشابه
Surfaces containing two circles through each point and Pythagorean 6-tuples
We study analytic surfaces in 3-dimensional Euclidean space containing two circular arcs through each point. The problem of finding such surfaces traces back to the works of Darboux from XIXth century. We reduce finding all such surfaces to the algebraic problem of finding all Pythagorean 6-tuples of polynomials. The reduction is based on the Schicho parametrization of surfaces containing two c...
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Addressing the direct control of surface wettability has been a significant challenge for a variety of applications from self-cleaning surfaces to phase-change applications. Surface wettability has been traditionally modulated by installing surface nanostructures or changing their chemistry. Among numerous nanofabrication efforts, the chemical oxidation method is considered a promising approach...
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Previous work of the author has developed coordinates on bundles over the classical Teichmüller spaces of punctured surfaces and on the space of cosets of the Möbius group in the group of orientation-preserving homeomorphisms of the circle, and this work is surveyed here. Joint work with Dragomiř Sari´c is also sketched which extends these results to the setting of the Teichmüller space of the ...
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In the search for appropriate discretizations of surface theory it is crucial to preserve such fundamental properties of surfaces as their invariance with respect to transformation groups. We discuss discretizations based on Möbius invariant building blocks such as circles and spheres. Concrete problems considered in these lectures include the Willmore energy as well as conformal and curvature ...
متن کاملSurfaces with Orthogonal Families of Circles
The lines of curvature on a cyclide of Dupin are circular arcs. A surface which carries two orthogonal families of circular arcs must arise as an integral surface of an overdetermined exterior differential system. We show that the only solutions of this system are the cyclides of Dupin.
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2018
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-018-1739-z