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.
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.
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.
Güler, E., & Kişi, Ö. (2019). Astrohelicoidal Hypersurfaces in 4-space. Turkish Journal of Mathematics and Computer Science, 11, 40-45.
AMA
Güler E, Kişi Ö. Astrohelicoidal Hypersurfaces in 4-space. TJMCS. December 2019;11:40-45.
Chicago
Güler, Erhan, and Ömer Kişi. “Astrohelicoidal Hypersurfaces in 4-Space”. Turkish Journal of Mathematics and Computer Science 11, December (December 2019): 40-45.
EndNote
Güler E, Kişi Ö (December 1, 2019) Astrohelicoidal Hypersurfaces in 4-space. Turkish Journal of Mathematics and Computer Science 11 40–45.
IEEE
E. Güler and Ö. Kişi, “Astrohelicoidal Hypersurfaces in 4-space”, TJMCS, vol. 11, pp. 40–45, 2019.
ISNAD
Güler, Erhan - Kişi, Ömer. “Astrohelicoidal Hypersurfaces in 4-Space”. Turkish Journal of Mathematics and Computer Science 11 (December 2019), 40-45.
JAMA
Güler E, Kişi Ö. Astrohelicoidal Hypersurfaces in 4-space. TJMCS. 2019;11:40–45.
MLA
Güler, Erhan and Ömer Kişi. “Astrohelicoidal Hypersurfaces in 4-Space”. Turkish Journal of Mathematics and Computer Science, vol. 11, 2019, pp. 40-45.
Vancouver
Güler E, Kişi Ö. Astrohelicoidal Hypersurfaces in 4-space. TJMCS. 2019;11:40-5.