# Circular cone and its Gauss map

Miekyung Choi; Dong-Soo Kim; Young Ho Kim; Dae Won Yoon

Colloquium Mathematicae (2012)

- Volume: 129, Issue: 2, page 203-210
- ISSN: 0010-1354

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topMiekyung Choi, et al. "Circular cone and its Gauss map." Colloquium Mathematicae 129.2 (2012): 203-210. <http://eudml.org/doc/283499>.

@article{MiekyungChoi2012,

abstract = {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.},

author = {Miekyung Choi, Dong-Soo Kim, Young Ho Kim, Dae Won Yoon},

journal = {Colloquium Mathematicae},

keywords = {ruled surface; Gauss map; pointwise 1-type; circular cone},

language = {eng},

number = {2},

pages = {203-210},

title = {Circular cone and its Gauss map},

url = {http://eudml.org/doc/283499},

volume = {129},

year = {2012},

}

TY - JOUR

AU - Miekyung Choi

AU - Dong-Soo Kim

AU - Young Ho Kim

AU - Dae Won Yoon

TI - Circular cone and its Gauss map

JO - Colloquium Mathematicae

PY - 2012

VL - 129

IS - 2

SP - 203

EP - 210

AB - 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.

LA - eng

KW - ruled surface; Gauss map; pointwise 1-type; circular cone

UR - http://eudml.org/doc/283499

ER -

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