scholarly journals On Minimal Surfaces Immersed in Three Dimensional Kropina Minkowski Space

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Ranadip Gangopadhyay ◽  
Ashok Kumar ◽  
Bankteshwar Tiwari
Keyword(s):  
Minkowski Space ◽  
Minimal Surfaces ◽  
Three Dimensional

scholarly journals $d$-Minimal Surfaces in Three-Dimensional Singular Semi-Euclidean Space $\mathbb{R}^{0,2,1}$

2021 ◽  
Vol 52 (1) ◽  
pp. 37-67
Author(s):  
Yuichiro Sato
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Minimal Surfaces ◽  
Mean Curvature ◽  
Three Dimensional ◽  
Representation Formula ◽  
Degenerate Metric ◽  
Dimensional Minkowski Space ◽  
One To One ◽  
Zero Mean Curvature

In this paper, we investigate surfaces in singular semi-Euclidean space $\mathbb{R}^{0,2,1}$ endowed with a degenerate metric. We define $d$-minimal surfaces, and give a representation formula of Weierstrass type. Moreover, we prove that $d$-minimal surfaces in $\mathbb{R}^{0,2,1}$ and spacelike flat zero mean curvature (ZMC) surfaces in four-dimensional Minkowski space $\mathbb{R}^{4}_{1}$ are in one-to-one correspondence.

scholarly journals Ruled minimal surfaces in the three-dimensional Heisenberg group

2013 ◽  
Vol 261 (2) ◽  
pp. 477-496 ◽  
Author(s):  
Heayong Shin ◽  
Young Wook Kim ◽  
Sung-Eun Koh ◽  
Hyung Yong Lee ◽  
Seong-Deog Yang
Keyword(s):  
Heisenberg Group ◽  
Minimal Surfaces ◽  
Three Dimensional
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