Timelike Minimal Surfaces via Loop Groups
Jun-ichi Inoguchi,Magdalena Toda +1 more
TLDR
In this article, the authors give a systematic study of Lorentz conformal structure from structural viewpoints, and apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for time-like minimal surfaces.Abstract:
This work consists of two parts. In Part I, we shall give a systematic study of Lorentz conformal structure from structural viewpoints. We study manifolds with split-complex structure. We apply general results on split-complex structure for the study of Lorentz surfaces. In Part II, we study the conformal realization of Lorentz surfaces in the Minkowski 3-space via conformal minimal immersions. We apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for timelike minimal surfaces. Classical integral representation formula for timelike minimal surfaces will be recovered from loop group theoretic viewpoint.read more
Citations
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Maximal surfaces with singularities in Minkowski space
Masaaki Umehara,Kotaro Yamada +1 more
TL;DR: In this paper, the authors investigated maximal surfaces in Minkowski 3-space with singularities and showed that they satisfy an Osserman-type inequality, which is the only complete maximal surface without singular points.
Journal ArticleDOI
The roots of a split quaternion
TL;DR: De Moivre’s formula forsplit quaternions is expressed and roots of a split quaternion are found using this formula.
Journal ArticleDOI
Björling problem for timelike surfaces in the Lorentz–Minkowski space
TL;DR: In this article, a split-complex representation for timelike surfaces in the Lorentz-Minkowski space is presented. But the problem is not solved in the present paper.
Journal ArticleDOI
Immersions of Lorentzian surfaces in R2,1
TL;DR: In this paper, the authors proved the equivalence between the data of a spacelike conformal immersion of a given Lorentzian surface into R 2, 1 and two spinors satisfying a Dirac-type equation on the surface.
Journal ArticleDOI
Zero mean curvature surfaces in L 3 containing a light-like line
Shoichi Fujimori,Young Wook Kim,Sung-Eun Koh,Wayne Rossman,Heayong Shin,H. Takahashi,Masaaki Umehara,Kotaro Yamada,Seong-Deog Yang +8 more
TL;DR: In this paper, the singular set of a light-like line has been analyzed in the context of space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski 3-space L 3.
References
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TL;DR: In this article, the Clifford algebras of real quadratic forms and their complexifications are studied in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context.
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