Geodesic
A classification of minimal translation surfaces in Minkowski space
Yang, Dan 1 ; Dan, Wei 2 ; Fu, Yu 3
1 School of Mathematics, Liaoning University, Shenyang, P. R. China
2 School of Mathematics and Statistic, Guangdong University of Finance and Economics, Guangzhou, P. R. China;Faculty of Arts and Sciences, Shenzhen Technology University, Shenzhen, P. R. China
3 School of Mathematics, Dongbei University of Finance and Economics, Dalian, P. R. China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 3, p. 437-443.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Minimal surfaces are well known as a class of surfaces with vanishing mean curvature which minimize area within a given boundary configuration since 19th century. This fact was implicitly proved by Lagrange for nonparametric surfaces in 1760, and then by Meusnier in 1776 who used the analytic expression for the mean curvature. Mathematically, a minimal surface corresponds to the solution of a nonlinear partial differential equation. By solving some differential equations, in this paper we give a complete and explicit classification of minimal translation surfaces in an $n$-dimensional Minkowski space.
DOI : 10.22436/jnsa.011.03.12
Classification : 53A10
Keywords: Minimal surfaces, translation surfaces, Minkowski space

Yang, Dan  1 ; Dan, Wei  2 ; Fu, Yu  3

1 School of Mathematics, Liaoning University, Shenyang, P. R. China
2 School of Mathematics and Statistic, Guangdong University of Finance and Economics, Guangzhou, P. R. China;Faculty of Arts and Sciences, Shenzhen Technology University, Shenzhen, P. R. China
3 School of Mathematics, Dongbei University of Finance and Economics, Dalian, P. R. China 
@article{JNSA_2018_11_3_a11,
     author = {Yang, Dan  and Dan, Wei  and Fu, Yu },
     title = {A classification of minimal translation surfaces in {Minkowski}  space},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {437-443},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2018},
     doi = {10.22436/jnsa.011.03.12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.03.12/}
}
TY  - JOUR
AU  - Yang, Dan 
AU  - Dan, Wei 
AU  - Fu, Yu 
TI  - A classification of minimal translation surfaces in Minkowski  space
JO  - Journal of nonlinear sciences and its applications
PY  - 2018
SP  - 437
EP  - 443
VL  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.03.12/
DO  - 10.22436/jnsa.011.03.12
LA  - en
ID  - JNSA_2018_11_3_a11
ER  - 
%0 Journal Article
%A Yang, Dan 
%A Dan, Wei 
%A Fu, Yu 
%T A classification of minimal translation surfaces in Minkowski  space
%J Journal of nonlinear sciences and its applications
%D 2018
%P 437-443
%V 11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.03.12/
%R 10.22436/jnsa.011.03.12
%G en
%F JNSA_2018_11_3_a11
Yang, Dan ; Dan, Wei ; Fu, Yu . A classification of minimal translation surfaces in Minkowski  space. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 3, p. 437-443. doi : 10.22436/jnsa.011.03.12. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.03.12/

[1] Bueno, A.; López, R. Translation surfaces of linear Weingarten type, arXive, Volume 2014 (2014), pp. 1-7

[2] Chen, B.-Y. Geometry of Submanifolds, Marcel Dekker, New York, 1973 | Zbl

[3] Chen, B.-Y. Pseudo-Riemannian Geometry, \(\delta\) -invariants and Applications, With a foreword by Leopold Verstraelen, World Scientific Publishing Co., Hackensack, 2011 | Zbl

[4] Dillen, F.; Verstraelen, L.; Zafindratafa, G. A generalization of the translation surfaces of Scherk, Diff. Geom. in honor of Radu Rosca (KUL) (1991), pp. 107-109 | Zbl

[5] Goemans, W. Surfaces in three-dimensional Euclidean and Minkowski space, in particular a study of Weingarten surfaces, PhD Thesis, Katholieke Univ. Leuven, Leuven, 2010

[6] Lima, B. P.; Santos, N. L.; Sousa, P. A. Translation hypersurfaces with constant scalar curvature into the Euclidean space, Israel J. Math., Volume 201 (2014), pp. 797-811 | DOI | Zbl

[7] Liu, H. Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom., Volume 64 (1999), pp. 141-149 | DOI | Zbl

[8] Marin, M. On weak solutions in elasticity of dipolar bodies with voids, J. Comp. Appl. Math., Volume 82 (1997), pp. 291-297 | Zbl | DOI

[9] Marin, M. Harmonic vibrations in thermoelasticity of microstretch materials, J. Vib. Acoust. ASME, 2010 (2010), 6 pages, Volume 2010 (2010), pp. 1-6 | DOI

[10] Munteanu, M. I.; Nistor, A. I. Polynomial Translation Weingarten Surfaces in 3-dimensional Euclidean space, Differential geometry, 316–320, World Sci. Publ., Hackensack, NJ, 2009 | Zbl | DOI

[11] Seo, K. Translation hypersurfaces with constant curvature in space forms, Osaka J. Math., Volume 50 (2013), pp. 631-641 | Zbl

[12] Sharma, K.; Marin, M. Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., Volume 75 (2013), pp. 121-132 | Zbl

[13] Verstraelen, L.; Walrave, J.; Yaprak, S. The minimal translation surfaces in Euclidean space, Soochow J. Math., Volume 20 (1994), pp. 77-82 | Zbl

Cité par Sources :