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

Creative Commons License

Duldul B. U.

FILOMAT, vol.32, no.17, pp.5827-5836, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 17
  • Publication Date: 2018
  • Doi Number: 10.2298/fil1817827u
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5827-5836
  • Yıldız Technical University Affiliated: Yes

Abstract

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.