• 제목/요약/키워드: Galilean 4-space

검색결과 6건 처리시간 0.021초

AN APPROACH FOR HYPERSURFACE FAMILY WITH COMMON GEODESIC CURVE IN THE 4D GALILEAN SPACE G4

  • Yoon, Dae Won;Yuzbasi, Zuhal Kucukarslan
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제25권4호
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    • pp.229-241
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    • 2018
  • 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.

A NOTE ON INEXTENSIBLE FLOWS OF CURVES WITH FERMI-WALKER DERIVATIVE IN GALILEAN SPACE G3

  • Bozok, Hulya Gun;Sertkol, Ipek Nizamettin
    • 호남수학학술지
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    • 제42권4호
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    • pp.769-780
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    • 2020
  • In this paper, Fermi-Walker derivative for inextensible flows of curves are researched in 3-dimensional Galilean space G3. Firstly using Frenet and Darboux frame with the help of Fermi-Walker derivative a new approach for these flows are expressed, then some results are obtained for these flows to be Fermi-Walker transported in G3.

TRANSLATION SURFACES IN THE 3-DIMENSIONAL GALILEAN SPACE SATISFYING ∆IIxiixi

  • Cakmak, Ali;Karacan, Murat Kemal;Kiziltug, Sezai;Yoon, Dae Won
    • 대한수학회보
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    • 제54권4호
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    • pp.1241-1254
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    • 2017
  • In this paper, we classify translation surfaces in the three dimensional Galilean space ${\mathbb{G}}_3$ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the second fundamental form of the surface. We also give explicit forms of these surfaces.