# Circular cone and its Gauss map

Colloquium Mathematicae (2012)

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

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## Abstract

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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.

## How to cite

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Miekyung 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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