Öz
We consider an astrohelicoidal hypersurface which its profile curve has astroid curve in the four dimensional Euclidean space ${\mathbb{E}}^{4}$. We also calculate Gaussian curvature and the mean curvature, and Weingarten relation of the hypersurface. Moreover, projecting hypersurface into 3-spaces, we draw some figures.
Anahtar Kelimeler
astrohelicoidal hypersurface Gauss map Gaussian curvature mean curvature
Kaynakça
- Arslan, K., K\i l\i \c{c} Bayram, B., Bulca, B., \"{O}zt\"{u}rk, G., \textit{Generalized rotation surfaces in $\mathbb{E}^{4}$}, Results Math., \textbf{61}(2012), 315--327.
- Eisenhart, L.P., A Treatise on the Differential Geometry of Curves and Surfaces, Dover Publications, N.Y., 1909.
- Forsyth, A.R., Lectures on the Differential Geometry of Curves and Surfaces, Cambridge Un. press, 2nd ed. 1920.
- Ganchev, G., Milousheva, V., \textit{General rotational surfaces in the 4-dimensional Minkowski space}, Turk. J. Math., \textbf{38}(2014), 883--895.
- Gray, A., Salamon, S., Abbena, E., Modern Differential Geometry of Curves and Surfaces with Mathematica, Third ed. Chapman \& Hall/CRC Press, Boca Raton, 2006.
- G\"{u}ler, E., Hac\i saliho{\u{g}}lu, H.H., Kim, Y.H., \textit{The Gauss map and the third Laplace-Beltrami operator of the rotational hypersurface in 4-Space}, Symmetry, \textbf{10(9)}(2018), 1--11.
- G\"{u}ler, E., Magid, M., Yayl\i, Y., \textit{Laplace Beltrami operator of a helicoidal hypersurface in four space}, J. Geom. Sym. Phys., \textbf{41}(2016), 77--95.
- G\"{u}ler, E., Turgay, N.C., {\em Cheng-Yau operator and Gauss map of rotational hypersurfaces in 4-space}, Mediterr. J. Math., \textbf{16(3)}(2019), 1--16.
- Hac\i saliho{\u{g}}lu, H.H., Diferensiyel Geometri I, Ankara {\"U}n., Ankara, 1982.
- Nitsche, J.C.C., Lectures on Minimal Surfaces. Vol. 1, Introduction, Fundamentals, Geometry and Basic Boundary Value Problems, Cambridge Un. Press, Cambridge, 1989.
Öz
Kaynakça
- Arslan, K., K\i l\i \c{c} Bayram, B., Bulca, B., \"{O}zt\"{u}rk, G., \textit{Generalized rotation surfaces in $\mathbb{E}^{4}$}, Results Math., \textbf{61}(2012), 315--327.
- Eisenhart, L.P., A Treatise on the Differential Geometry of Curves and Surfaces, Dover Publications, N.Y., 1909.
- Forsyth, A.R., Lectures on the Differential Geometry of Curves and Surfaces, Cambridge Un. press, 2nd ed. 1920.
- Ganchev, G., Milousheva, V., \textit{General rotational surfaces in the 4-dimensional Minkowski space}, Turk. J. Math., \textbf{38}(2014), 883--895.
- Gray, A., Salamon, S., Abbena, E., Modern Differential Geometry of Curves and Surfaces with Mathematica, Third ed. Chapman \& Hall/CRC Press, Boca Raton, 2006.
- G\"{u}ler, E., Hac\i saliho{\u{g}}lu, H.H., Kim, Y.H., \textit{The Gauss map and the third Laplace-Beltrami operator of the rotational hypersurface in 4-Space}, Symmetry, \textbf{10(9)}(2018), 1--11.
- G\"{u}ler, E., Magid, M., Yayl\i, Y., \textit{Laplace Beltrami operator of a helicoidal hypersurface in four space}, J. Geom. Sym. Phys., \textbf{41}(2016), 77--95.
- G\"{u}ler, E., Turgay, N.C., {\em Cheng-Yau operator and Gauss map of rotational hypersurfaces in 4-space}, Mediterr. J. Math., \textbf{16(3)}(2019), 1--16.
- Hac\i saliho{\u{g}}lu, H.H., Diferensiyel Geometri I, Ankara {\"U}n., Ankara, 1982.
- Nitsche, J.C.C., Lectures on Minimal Surfaces. Vol. 1, Introduction, Fundamentals, Geometry and Basic Boundary Value Problems, Cambridge Un. Press, Cambridge, 1989.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Aralık 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 11 |
