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Abstrakty
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.
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Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
203-210
Opis fizyczny
Daty
wydano
2012
Twórcy
autor
- Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Korea
autor
- Department of Marthematics, Chonnam National University, Kwangju 500-757, Korea
autor
- Department of Marthematics, Kyungpook National University, Taegu 702-701, Korea
autor
- Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Korea
Bibliografia
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-2-4