Type I + Helicoidal Surfaces with Prescribed Weighted Mean or Gaussian Curvature in Minkowski Space with Density-Reference-Cited by-同舟云学术

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

Published:2018-12-01 Issue:3 Volume:26 Page:99-108
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Yıldız Önder Gökmen¹,Hızal Selman²,Akyiğit Mahmut³

Affiliation:

1. Department of Mathematics, Faculty of Arts and Science , Bilecik Şeyh Edebali University , Gülümbe Campus, 11230 Bilecik , Turkey .

2. Distance Education Research And Application Centre , Sakarya University , Esentepe Campus, 54187 Sakarya , Turkey .

3. Department of Mathematics, Faculty of Arts and Science , Sakarya University , Esentepe Campus, 54187 Sakarya , Turkey .

Abstract

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

ℝ 1 3

${\Bbb R}_1^3$

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2018-0035

Reference15 articles.

1. [1] C. Baikoussis, T. Koufogiorgos, Helicoidal surfaces with prescribed mean or Gaussian curvature, Journal of Geometry 63.(1) (1998) 25-29.10.1007/BF01221235

2. [2] C. C. Beneki, G. Kaimakamis, B. J. Papantoniou, Helicoidal surfaces in three-dimensional Minkowski space, Journal of Mathematical Analysis and Applications 275.(2) (2002) 586-614.10.1016/S0022-247X(02)00269-X

3. [3] I. Corwin, N. Hoffman, S. Hurder, V. eum, Y. Xu, Differential geometry of manifolds with density. Rose-Hulman Undergrad. Math. J. 7 (2006) 1-15.

4. [4] M. P. Do Carmo, M. Dajczer, Helicoidal surfaces with constant mean curvature, Tohoku Mathematical Journal, Second Series 34.(3) (1982) 425-435.10.2748/tmj/1178229204

5. [5] C. H. Delaunay, Sur la surface de révolution dont la courbure moyenne est constante, Journal de mathématiques pures et appliquées (1841) 309-314.

Cited by 8 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Generalized rotation surfaces in E4 with density;Journal of Geometry and Physics;2023-04

2. On the Gaussian curvature of timelike surfaces in Lorentz-Minkowski 3-space;Filomat;2023

3. Helicoidal surfaces in some conformally flat pseudo-spaces of dimensional three;International Journal of Geometric Methods in Modern Physics;2022-12-03

4. Offset Ruled Surface in Euclidean Space with Density;Analele Universitatii "Ovidius" Constanta - Seria Matematica;2021-03-01

5. Rotational Hypersurfaces in Euclidean 4-Space with Density;Journal of Polytechnic;2020-10-27