Circular cone and its Gauss map

• Autorzy: Miekyung Choi , Dong-Soo Kim , Young Ho Kim , Dae Won Yoon
• Języki publikacji: EN

Abstrakty

EN

The family of cones is one of typical models of non-cylindrical ruled surfaces. Among them, the circular cones are unique in the sense that their Gauss map satisfies a partial differential equation similar, though not identical, to one characterizing the so-called 1-type submanifolds. Specifically, for the Gauss map G of a circular cone, one has ΔG = f(G+C), where Δ is the Laplacian operator, f is a non-zero function and C is a constant vector. We prove that circular cones are characterized by being the only non-cylindrical ruled surfaces with ΔG = f(G+C) for a nonzero constant vector C.

Kategorie tematyczne

• 53B25: Local submanifolds
• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 129
• Numer: 2
• Strony: 203-210

Daty

wydano

2012

Twórcy

autor

Miekyung Choi

• Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Korea

autor

Dong-Soo Kim

• Department of Marthematics, Chonnam National University, Kwangju 500-757, Korea

autor

Young Ho Kim

• Department of Marthematics, Kyungpook National University, Taegu 702-701, Korea

autor

Dae Won Yoon

• Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Korea

Identyfikatory

DOI

10.4064/cm129-2-4