A New Method for Finding the Shape Operator of a Hypersurface in Euclidean 4-Space


Duldul B. U.

FILOMAT, cilt.32, no.17, ss.5827-5836, 2018 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 32 Konu: 17
  • Basım Tarihi: 2018
  • Doi Numarası: 10.2298/fil1817827u
  • Dergi Adı: FILOMAT
  • Sayfa Sayısı: ss.5827-5836

Özet

In this paper, by taking a Frenet curve lying on a parametric or implicit hypersurface and using the extended Darboux frame field of this curve, we give a new method for calculating the shape operator's matrix of the hypersurface depending on the extended Darboux frame curvatures. This new method enables us to obtain the Gaussian and mean curvatures of the hypersurface depending on the geodesic torsions of the curve and the normal curvatures of the hypersurface.