4-boyutlu Öklid Uzayında Kapalı Hiperyüzeylerin Eğrilikleri

Bu çalışmada, 4-boyutlu Öklid uzayında bir hiperyüzeyin Gauss ve ortalama eğrilikleri çalışılmıştır.

Anahtar Kelimeler:

Gauss eğriliği, hiperyüzey, ortalama eğrilik

Curvatures of Implicit Hypersurfaces in Euclidean 4-space

In this paper, we study the Gaussian and the mean curvatures of a hypersurface in Euclidean 4-space.We obtain the formulas of these curvatures by using the Riemannian connection of Euclidean 4-space. As an applicationof the obtained formulas, we give the Gaussian and mean curvatures of an implicit hypersurface. Also, theGaussian curvatures of some quadric hypersurfaces are given.

Keywords:

Gaussian curvature, hypersurface, mean curvature,

PDF

___

Gray A, Abbena E, Salamon S, 2006. Modern differential Geometry of Curves and Surfaces with Mathematica. Third Edition, Boca Raton, USA. 1016 p.
Hollasch SR, 1991. Four-space visualization of 4D objects. Arizona State University, Master Thesis, 182p. Lee JM, 1997. Riemannian manifolds. New York, USA. 224 p.
Sotomayor J, Garcia R, 2016. Lines of Curvature on Quadric Hypersurfaces of Lobachevskii Journal of Mathematics, 37: 288-306.
Williams MZ, Stein FM, 1964. A triple product of vectors in four-space. Mathematics Magazine, 37: 230-235.