Abstract
In this paper, we study the hypersurface families with Smarandache curves in 4-dimensional Galilean space G 4 and give the conditions for different Smarandache curves to be parameter and the curve which generates the Smarandache curves is geodesic on a hypersurface in G 4 . Also, we investigate three types of marching-scale functions for one of these hypersurfaces and construct an example for it.
Highlights
In physics, geodesics which are de...ned as a parallel transport of a tangent vector in a linear (a¢ ne) connection on the manifold M are very important for general relativity
The problem of constructing a family of surfaces from a given spatial geodesic curve ...rstly has been studied by Wang et al in 2004 and in that study, the authors have derived a parametric representation for a surface pencil whose members share the same geodesic curve as an isoparametric curve [15]
We investigate the hypersurface families with Smarandache curves in 4-dimensional Galilean space G4: 2. HYPERSURFACE FAMILIES WITH SMARANDACHE CURVES IN 4-DIMENSIONAL GALILEAN SPACE G4
Summary
Geodesics which are de...ned as a parallel transport of a tangent vector in a linear (a¢ ne) connection on the manifold M are very important for general relativity.
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