Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space
Rafael López
- Vol. 7, Iss: 1, pp 44-107
TLDR
In this article, the authors review part of the classical theory of curves and surfaces in 3D Lorentz-Minkowski space and focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.Abstract:
We review part of the classical theory of curves and surfaces in 3-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.read more
Citations
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Translation and homothetical surfaces in euclidean space with constant curvature
Rafael López,Marilena Moruz +1 more
TL;DR: This work considers the problem to determine all surfaces in Euclidean space constructed by the sum of two curves or that are graphs of the product of two functions with constant Gauss curvature that are non degenerate surfaces in Lorentz-Minkowski space.
Posted Content
Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space
TL;DR: In this article, the authors review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space and focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.
Journal ArticleDOI
Moving frames and the characterization of curves that lie on a surface
TL;DR: In this paper, the authors apply these ideas to surfaces that are implicitly defined by a smooth function, by reinterpreting the problem in the context of the Hessian of F, which is not always positive definite.
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Geometric Formulation and Multi‐dark Soliton Solution to the Defocusing Complex Short Pulse Equation
TL;DR: In this article, the authors derived the defocusing CSP equation from the single component extended Kadomtsev-Petviashvili (KP) hierarchy by the reduction method.
Journal ArticleDOI
On (contra)pedals and (anti)orthotomics of frontals in de Sitter 2‐space
Yanlin Li,O. Oğulcan Tuncer +1 more
TL;DR: In this article , the de Sitter Legendrian Frenet frames were used to provide parametric representations of (contra)pedal curves of spacelike and timelike frontals in the deSitter 2-space and to investigate the geometric and singularity properties of these (contraspedal) curves.
References
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