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## Circular cone and its Gauss map

### Tom 129 / 2012

Colloquium Mathematicum 129 (2012), 203-210 MSC: Primary 53B25; Secondary 53C40. DOI: 10.4064/cm129-2-4

#### Streszczenie

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 $\varDelta G = f(G+C)$, where $\varDelta$ 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 $\varDelta G = f(G+C)$ for a nonzero constant vector $C$.

#### Autorzy

• Miekyung ChoiDepartment of Mathematics Education and RINS
Gyeongsang National University
Jinju 660-701, Korea
e-mail
• Dong-Soo KimDepartment of Marthematics
Chonnam National University
Kwangju 500-757, Korea
e-mail
• Young Ho KimDepartment of Marthematics
Kyungpook National University
Taegu 702-701, Korea
e-mail
• Dae Won YoonDepartment of Mathematics Education and RINS
Gyeongsang National University
Jinju 660-701, Korea
e-mail

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