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.
Anahtar Kelimeler
Shape operator vector product ternary product Dupin indicatrix Weingarten Map
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.
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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 5 Şubat 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 1 Sayı: 1 |
