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Surfaces which contain many circles

Nobuko Takeuchi (2008)

Banach Center Publications

We survey the results on surfaces which contain many circles. First, we give two analyses of shapes which always look round. Then we introduce the Blum conjecture: “A closed C surface in E³ which contains seven circles through each point is a sphere”, and give some partial affirmative results toward the conjecture. Moreover, we study some surfaces which contain many circles through each point, for example, cyclides.

Surfaces with non-zero normal curvature tensor

Antonio Carlos Asperti, Dirk Ferus, Lucio Rodriguez (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Studiamo la topologia differenziale e la geometria delle superfici compatte con curvatura normale non-nulla in spazio della curvatura costante.

Surfaces with prescribed Weingarten operator

Udo Simon, Konrad Voss, Luc Vrancken, Martin Wiehe (2002)

Banach Center Publications

We investigate pairs of surfaces in Euclidean 3-space with the same Weingarten operator in case that one surface is given as surface of revolution. Our local and global results complement global results on ovaloids of revolution from S-V-W-W.

Symmetric algebras and Yang-Baxter equation

Beidar, K., Fong, Y., Stolin, A. (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

Let U be an open subset of the complex plane, and let L denote a finite-dimensional complex simple Lie algebra. A. A. Belavin and V. G. Drinfel’d investigated non-degenerate meromorphic functions from U × U into L L which are solutions of the classical Yang-Baxter equation [Funct. Anal. Appl. 16, 159-180 (1983; Zbl 0504.22016)]. They found that (up to equivalence) the solutions depend only on the difference of the two variables and that their set of poles forms a discrete (additive) subgroup Γ of the...

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