Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

Rafael López; Esma Demir

Open Mathematics (2014)

  • Volume: 12, Issue: 9, page 1349-1361
  • ISSN: 2391-5455

Abstract

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We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.

How to cite

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Rafael López, and Esma Demir. "Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature." Open Mathematics 12.9 (2014): 1349-1361. <http://eudml.org/doc/269080>.

@article{RafaelLópez2014,
abstract = {We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.},
author = {Rafael López, Esma Demir},
journal = {Open Mathematics},
keywords = {Minkowski space; Helicoidad surface; Mean curvature; Gauss curvature; helicoidad surface; mean curvature},
language = {eng},
number = {9},
pages = {1349-1361},
title = {Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature},
url = {http://eudml.org/doc/269080},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Rafael López
AU - Esma Demir
TI - Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature
JO - Open Mathematics
PY - 2014
VL - 12
IS - 9
SP - 1349
EP - 1361
AB - We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.
LA - eng
KW - Minkowski space; Helicoidad surface; Mean curvature; Gauss curvature; helicoidad surface; mean curvature
UR - http://eudml.org/doc/269080
ER -

References

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