Rotational Hypersurfaces in S3(r)XR Product Space Bölüm Araştırma Makalesi

Year 2017, Volume: 21 Issue: 3, 350 - 355, 01.06.2017

Erhan Güler Ömer Kişi

https://doi.org/10.16984/saufenbilder.284219

Abstract

 Beş boyutlu Öklid uzayı  içindeki  çarpım uzayının
dönel hiperyüzeylerini ele aldık. Hiperyüzeylerin ortalama eğriliği ve Gauss
eğriliğini hesapladık ve bunların bazı sonuçlarını verdik 

Keywords

5-boyut, dönel hiperyüzey, şekil operatörü, Gauss eğriliği, ortalama eğrilik

Rotational Hypersurfaces in S3(r)R Product Space

Abstract

We consider rotational hypersurfaces in S3(r) R product space of five dimensional Euclidean space E5. We
calculate the mean curvature and the Gaussian curvature, and give some results  

Keywords

5-space, rotational hypersurface, shape operator, Gaussian curvature, mean curvature

References

• [1] Arslan K., Kılıç Bayram B., Bulca B., Öztürk G. Generalized Rotation Surfaces in Result Math. 61 (2012) 315-327.
• [2] Bour E. Théorie de la déformation des surfaces. J. de l.Êcole Imperiale Polytechnique 22-39 (1862) 1-148.
• [3] Cheng Q.M., Wan Q.R. Complete hypersurfaces of with constant mean curvature. Monatsh. Math. 118 (1994) 3-4, 171-204.
• [4] Do Carmo M., Dajczer M. Helicoidal surfaces with constant mean curvature. Tohoku Math. J. 34 (1982) 351-367.
• [5] Ganchev G., Milousheva, V. General rotational surfaces in the 4-dimensional Minkowski space. Turkish J. Math. 38 (2014) 883-895.
• [6] Magid M., Scharlach C., Vrancken L. Affine umbilical surfaces in Manuscripta Math. 88 (1995) 275-289.
• [7] Moore C. Surfaces of rotation in a space of four dimensions. Ann. Math. 21 (1919) 81-93.
• [8] Moore C. Rotation surfaces of constant curvature in space of four dimensions. Bull. Amer. Math. Soc. 26 (1920) 454-460.
• [9] Moruz M., Munteanu M.I. Minimal translation hypersurfaces in J. Math. Anal. Appl. 439 (2016) 798-812.
• [10] O'Neill, B. Elementary Differential Geometry. Revised second edition. Elsevier/Academic Press, Amsterdam, (2006).
• [11] Scharlach, C. Affine geometry of surfaces and hypersurfaces in . Symposium on the Differential Geometry of Submanifolds, France (2007) 251-256.
• [12] Vlachos Th. Hypersurfaces in with harmonic mean curvature vector field. Math. Nachr. 172 (1995) 145-169.