Rotational Hypersurfaces in S ( ) R 3 r Product Space

We consider rotational hypersurfaces in S ( ) R 3 r product space of five dimensional Euclidean space . 5 E We calculate the mean curvature and the Gaussian curvature, and give some results

S ( ) R 3 r Çarpım Uzayındaki Dönel Hiperyüzeyler

Beş boyutlu Öklid uzayı 5 E içindeki S ( ) R 3 r çarpım uzayının dönel hiperyüzeylerini ele aldık. Hiperyüzeylerin ortalama eğriliği ve Gauss eğriliğini hesapladık ve bunların bazı sonuçlarını verdik

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K. Arslan, B. Kılıç Bayram, B. Bulca, G. Öztürk, “Generalized Rotation Surfaces in 4 E ,” Result Math. vol. 61, pp. 315–327, 2012.

E. Bour, “Théorie de la déformation des surfaces,” J. de l.Êcole Imperiale Polytechnique vol. 22, no. 39, pp. 1–148, 1862.

Q.M. Cheng, Q.R. Wan, “Complete hypersurfaces of 4 R with constant mean curvature,” Monatsh. Math. vol. 118, no. 3-4, pp. 171–204, 1994.

M. Do Carmo, M. Dajczer, “Helicoidal surfaces with constant mean curvature,” Tohoku Math. J. vol. 34 pp. 351–367, 1982.

G. Ganchev, V. Milousheva, “General rotational surfaces in the 4-dimensional Minkowski space,” Turkish J. Math. vol. 38, pp. 883–895, 2014.

M. Magid, C. Scharlach, L. Vrancken, “Affine umbilical surfaces in 4 R ,” Manuscripta Math. vol. 88, pp. 275–289, 1995.

C. Moore, “Surfaces of rotation in a space of four dimensions,” Ann. Math. vol. 21, pp. 81–93, 1919.

C. Moore, “Rotation surfaces of constant curvature in space of four dimensions,” Bull. Amer. Math. Soc. Vol. 26, pp. 454–460, 1920.

M. Moruz, M.I. Munteanu, “Minimal translation hypersurfaces in 4 E ,” J. Math. Anal. Appl. vol. 439, pp. 798–812, 2016.

B. O'Neill, “Elementary Differential Geometry,” Revised second edition, Elsevier/Academic Press, Amsterdam, 2006.

C. Scharlach, “Affine geometry of surfaces and hypersurfaces in 4 R ,” Symposium on the Differential Geometry of Submanifolds, France, pp. 251–256, 2007.

Th. Vlachos, “Hypersurfaces in 4 E with harmonic mean curvature vector field,” Math. Nachr. vol. 172, pp. 145–169, 1995.