Classifications of helicoidal surfaces with l1-pointwise 1-type gauss map

Young Ho Kim; Nurettin Cenk Turgay

doi:10.4134/BKMS.2013.50.4.1345

Classifications of helicoidal surfaces with l1-pointwise 1-type gauss map

Young Ho Kim, Nurettin Cenk Turgay

Department of Mathematics Engineering

Kyungpook National University

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps G satisfy L₁G = f(G+C) for some constant vector C ∈ E³ and smooth function f, where L₁ denotes the Cheng-Yau operator.

Original language	English
Pages (from-to)	1345-1356
Number of pages	12
Journal	Bulletin of the Korean Mathematical Society
Volume	50
Issue number	4
DOIs	https://doi.org/10.4134/BKMS.2013.50.4.1345
Publication status	Published - 2013

Keywords

Cheng-yau operator
Gauss map
Helicoidal surface
L1-pointwise 1-type
Lie point symmetry
Rotational surface

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10.4134/BKMS.2013.50.4.1345

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abstract = "In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps G satisfy L1G = f(G+C) for some constant vector C ∈ E3 and smooth function f, where L1 denotes the Cheng-Yau operator.",

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AB - In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps G satisfy L1G = f(G+C) for some constant vector C ∈ E3 and smooth function f, where L1 denotes the Cheng-Yau operator.

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KW - Gauss map

KW - Helicoidal surface

KW - L1-pointwise 1-type

KW - Lie point symmetry

KW - Rotational surface

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ER -

Classifications of helicoidal surfaces with l1-pointwise 1-type gauss map

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Keywords

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