Surfaces which contain many circles

• Autorzy: Nobuko Takeuchi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53A05: Surfaces in Euclidean space
• 53A30: Conformal differential geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 82
• Numer: 1
• Strony: 201-207

Daty

wydano

2008

Twórcy

autor

Nobuko Takeuchi

• Department of Mathematics, Tokyo Gakugei University, Koganei-shi, Tokyo, 184-8501, Japan

Identyfikatory

DOI

10.4064/bc82-0-14