<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we construct a helicoidal surface of type <italic>I</italic>+ with prescribed weighted mean curvature and Gaussian curvature in the Minkowski 3<italic>−</italic>space <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_auom-2018-0035_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mrow><mo>ℝ</mo></mrow><mn>1</mn><mn>3</mn></msubsup></mrow></math><tex-math>${\Bbb R}_1^3$</tex-math></alternatives></inline-formula>with a positive density function. We get a result for minimal case. Also, we give examples of a helicoidal surface with weighted mean curvature and Gaussian curvature.</abstract>

In this paper, we construct a helicoidal surface of type I+ with prescribed weighted mean curvature and Gaussian curvature in the Minkowski 3−space ℝ13${\Bbb R}_1^3$with a positive density function. We get a result for minimal case. Also, we give examples of a helicoidal surface with weighted mean curvature and Gaussian curvature.

Type <italic>I</italic>+ Helicoidal Surfaces with Prescribed Weighted Mean or Gaussian Curvature in Minkowski Space with Density

Department of Mathematics, Faculty of Arts and Science

Distance Education Research And Application Centre

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Type  Helicoidal Surfaces with Prescribed Weighted Mean or Gaussian Curvature in Minkowski Space with Density

In this paper, we construct a helicoidal surface of type I+ with prescribed weighted mean curvature and Gaussian curvature in the Minkowski 3−space ℝ13${\Bbb...

Type I⁺ Helicoidal Surfaces with Prescribed Weighted Mean or Gaussian Curvature in Minkowski Space with Density

Published Online: Dec 31, 2018

Page range: 99 - 108

Received: Dec 02, 2017

Accepted: Jan 31, 2018

DOI: https://doi.org/10.2478/auom-2018-0035

Keywords
Minkowski space, manifold with density, weighted curvature, helicoidal

© 2018 Önder Gökmen Yıldız et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Type I+ Helicoidal Surfaces with Prescribed Weighted Mean or Gaussian Curvature in Minkowski Space with Density

Published Online: Dec 31, 2018

Page range: 99 - 108

Received: Dec 02, 2017

Accepted: Jan 31, 2018

DOI: https://doi.org/10.2478/auom-2018-0035

KeywordsMinkowski space, manifold with density, weighted curvature, helicoidal

© 2018 Önder Gökmen Yıldız et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Type I⁺ Helicoidal Surfaces with Prescribed Weighted Mean or Gaussian Curvature in Minkowski Space with Density

Keywords
Minkowski space, manifold with density, weighted curvature, helicoidal