Araştırma Makalesi
BibTex RIS Kaynak Göster

Weingarten Map of the Hypersurface in Euclidean 4-Space and its Applications

Yıl 2019, Cilt: 1 Sayı: 1, 1 - 8, 05.02.2019

Öz

In this paper, by taking into account the beginning of the hypersurface theory in Euclidean space E
4
, a practical
method for the matrix of the Weingarten map (or the shape operator) of an oriented hypersurface M3
in E
4
is
obtained. By taking this efficient method, it is possible to study of the hypersurface theory in E
4 which is analog
the surface theory in E
3
. Furthermore, the Gaussian curvature, Mean curvature, fundamental forms and Dupin
indicatrix of M3
is introduced.

Kaynakça

  • Al’essio O. Differential geometry of intersection curves in R4 of three implicit surfaces. Comput Aided Geom D 2009; 26:455-471.
  • Hollasch S.R. Four-space visualization of 4D objects. MSc, Arizona State University, Phoenix, AZ, USA, 1991.
  • Lee J.M., Riemann Manifolds, New York, USA, 1997.
  • Duldul B.U. Curvatures of implicit hypersurfaces in Euclidean 4-space. Igdir Univ. J. Inst. Sci. and Tech. 2018; 8(1):229-236.
  • Williams M.Z, Stein F.M. A triple product of vectors in four-space. Math Mag 1964; 37: 230-235.
Yıl 2019, Cilt: 1 Sayı: 1, 1 - 8, 05.02.2019

Öz

Kaynakça

  • Al’essio O. Differential geometry of intersection curves in R4 of three implicit surfaces. Comput Aided Geom D 2009; 26:455-471.
  • Hollasch S.R. Four-space visualization of 4D objects. MSc, Arizona State University, Phoenix, AZ, USA, 1991.
  • Lee J.M., Riemann Manifolds, New York, USA, 1997.
  • Duldul B.U. Curvatures of implicit hypersurfaces in Euclidean 4-space. Igdir Univ. J. Inst. Sci. and Tech. 2018; 8(1):229-236.
  • Williams M.Z, Stein F.M. A triple product of vectors in four-space. Math Mag 1964; 37: 230-235.
Toplam 5 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Salim Yüce

Yayımlanma Tarihi 5 Şubat 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 1 Sayı: 1

Kaynak Göster

APA Yüce, S. (2019). Weingarten Map of the Hypersurface in Euclidean 4-Space and its Applications. Hagia Sophia Journal of Geometry, 1(1), 1-8.