On the Gauss map of minimal Lorentzian surfaces in 4-dimensional semi-Riemannian space forms with index 2

Elif Özkara Canfes; Nurettin Cenk Turgay

doi:10.5486/PMD.2017.7643

On the Gauss map of minimal Lorentzian surfaces in 4-dimensional semi-Riemannian space forms with index 2

Elif Özkara Canfes, Nurettin Cenk Turgay

Department of Mathematics Engineering

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

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Abstract

In this paper, we study minimal Lorentzian surfaces with finite type Gauss map in 4-dimensional semi-Riemannian space forms with index of 2. First, we give the complete classification of Lorentzian surfaces in the semi-Euclidean space E⁴₂ with pointwise 1-type Gauss map. Then, we study all Lorentzian minimal surfaces in S⁴₂(1) regarding their Gauss map. In particular, we proved that a Lorentzian minimal surface in S⁴₂(1) has 2-type Gauss map if and only if it has constant Gaussian curvature and non-zero constant normal curvature.

Original language	English
Pages (from-to)	349-367
Number of pages	19
Journal	Publicationes Mathematicae Debrecen
Volume	91
Issue number	3-4
DOIs	https://doi.org/10.5486/PMD.2017.7643
Publication status	Published - 2017

Bibliographical note

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© 2017 University of Debrecen, Institute of Mathematics. All rights reserved.

Keywords

Finite type map
Finite type submanifolds
Lorentzian surface
Minimal surfaces
Minkowski space-time
Pointwise 1-type Gauss map
Semi-Riemannian space forms

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abstract = "In this paper, we study minimal Lorentzian surfaces with finite type Gauss map in 4-dimensional semi-Riemannian space forms with index of 2. First, we give the complete classification of Lorentzian surfaces in the semi-Euclidean space E42 with pointwise 1-type Gauss map. Then, we study all Lorentzian minimal surfaces in S42(1) regarding their Gauss map. In particular, we proved that a Lorentzian minimal surface in S42(1) has 2-type Gauss map if and only if it has constant Gaussian curvature and non-zero constant normal curvature.",

keywords = "Finite type map, Finite type submanifolds, Lorentzian surface, Minimal surfaces, Minkowski space-time, Pointwise 1-type Gauss map, Semi-Riemannian space forms",

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AU - Turgay, Nurettin Cenk

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AB - In this paper, we study minimal Lorentzian surfaces with finite type Gauss map in 4-dimensional semi-Riemannian space forms with index of 2. First, we give the complete classification of Lorentzian surfaces in the semi-Euclidean space E42 with pointwise 1-type Gauss map. Then, we study all Lorentzian minimal surfaces in S42(1) regarding their Gauss map. In particular, we proved that a Lorentzian minimal surface in S42(1) has 2-type Gauss map if and only if it has constant Gaussian curvature and non-zero constant normal curvature.

KW - Finite type map

KW - Finite type submanifolds

KW - Lorentzian surface

KW - Minimal surfaces

KW - Minkowski space-time

KW - Pointwise 1-type Gauss map

KW - Semi-Riemannian space forms

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JF - Publicationes Mathematicae Debrecen

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ER -

On the Gauss map of minimal Lorentzian surfaces in 4-dimensional semi-Riemannian space forms with index 2

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