Canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space
arXiv:1911.10779
Abstract
We introduce canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space and prove the existence and the uniqueness of these parameters. With respect to these coordinates the coefficients of the first fundamental form are expressed by the invariants of the surface. On any time-like surface we introduce a special complex function over the algebra of the double numbers and apply the analysis over the algebra of the double numbers as a convenient tool to study these surfaces. Then the canonical coordinates on minimal time-like surfaces are characterized by a natural condition for this complex function. We consider the hyperbola of the normal curvature of any minimal time-like surface and give a geometric interpretation of the canonical coordinates in terms of the elements of this hyperbola.
arXiv comment25 pages
References in corpus (6)
- On the Invariant Theory of Weingarten Surfaces in Euclidean Space
- Timelike surfaces with zero mean curvature in Minkowski 4-space
- Minimal Lorentz Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric
- Explicit Solving of the System of Natural PDE's of Minimal Surfaces in the Four-Dimensional Euclidean Space
- Explicit Solving of the System of Natural PDE's of Minimal Space-like Surfaces in Minkowski Space-time
- Canonical Weierstrass representations for minimal space-like surfaces in $\RR^4_1$