The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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AN APPROACH FOR HYPERSURFACE FAMILY WITH COMMON GEODESIC CURVE IN THE 4D GALILEAN SPACE G4

  • Received : 2017.09.05
  • Accepted : 2018.09.11
  • Published : 2018.11.30
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Abstract

In the present study, we derive the problem of constructing a hypersurface family from a given isogeodesic curve in the 4D Galilean space $G_4$. We obtain the hypersurface as a linear combination of the Frenet frame in $G_4$ and examine the necessary and sufficient conditions for the curve as a geodesic curve. Finally, some examples related to our method are given for the sake of clarity.

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SHGHCX_2018_v25n4_229_f0001.png 이미지

Figure 1. Projection of a member of the hypersurface family with marching-scale functions and its isogeodesic.

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