A Characterization of Factorable Surfaces in Euclidean 4-Space E^4

Year 2018, Volume: 1 Issue: 1 , 15 - 20 , 31.05.2018

Sezgin Büyükkütük , Günay Öztürk

https://doi.org/10.34088/kojose.403665

https://izlik.org/JA34DN37CG

Abstract

In this
paper, we consider a factorable surface in Euclidean E^4 with its curvature
ellipse. We classify the origin of the normal space of such a surface according
to whether it is hyperbolic, parabolic, or elliptic. Further, we give the
necessary and sufficient condition of the factorable surface to become Wintgen
ideal surface.

Keywords

Curvature ellipse , Factorable surface , Gaussian curvature , Mean curvature , Normal curvature , Wintgen ideal surface

References

• Chen B. Y., 1973. Geometry of Submanifolds. Marcel Dekker, New York.
• Gutierrez Nunez J.M., Romero Fuster M.C., Sanchez-Bringas F., 2008. Codazzi fields on surfaces immersed in Euclidean spaces. Osaka J. Math 45, 877‒894.
• Wintgen P., 1979.Sur 1’inegalite de Chen-Wilmore. C. R. Acad. Sci., Paris, 288, 993‒995.
• Arslan K., Bayram B.K., Bulca B., Öztürk G., 2012. Generalized rotation surfaces in . Results in Mathematics 61, 315‒327.
• Bayram B.K., Bulca B., Arslan K., Öztürk G., 2009. Superconformal ruled surfaces in . Math. Commun. 14, 235‒244.
• Bulca B., Arslan K., 2014. Semiparallel Wintgen ideal surfaces in . C. R. Acad. Bulgare Sci. 67, 613‒622.
• Bulca B., Arslan K., Bayram B.K., Öztürk G., 2012. Spherical product surface in . An. St. Univ. Ovidius Constanta 20, 41‒54.
• Chen B. Y., 2011. On Wintgen ideal surfaces, Proceedings of The Conference RIGA 2011, Riemannian Geometry and Applications, Bucharest, Romania, 10-14 May 2011, 59‒74.
• İyigün E., Arslan K., Öztürk G., 2018. A characterization of Chen surfaces in . Bull. Malays. Math. Math. Soc. 31, 209‒215.
• Woestyne I. V, 1993. A new characterization of helicoids. Geometry and topology submanifolds World Sci. Publ. River Edge, 267‒273.
• Woestyne I. V, 1995. Minimal homothetical hypersurfaces of a semi-Euclidean space. Results Math. 27 , 333‒342.
• Lopez R., Moruz M., 2015. Translation and homothetical surfaces in Euclidean spaces with constant curvature. J. Korean Math. Soc. 52, 523‒535.
• Meng H., Liu H. 2009.Factorable surfaces in Minkowski space. Bull. Korean Math. Soc. 46, 155‒169.
• Yu Y., Liu H., 2007. The factorable minimal surfaces. Proceedings of the Eleventh International Workshop on Diff. Geom. 11, 33‒39.
• Büyükkütük S., Öztürk G., 2017. Spacelike factorable surfaces in four-dimensional Minkowski space. Bulletin of Mathematical Analysis and Applications 9, 12‒20.
• Aminov Y. A., 1994. Surfaces in with a Gaussian curvature coinciding with a Gaussian torsion up to sign. Mathematical Notes 56(6), 5‒6.
• Bulca B., Arslan K., 2013. Surfaces given with the Monge patch in . Journal of Mathematical Physics, Analysis, Geometry 9, 435‒447.
• Little J.A., 1969. On singularities of submanifolds of higher dimensional Euclidean space. Ann. Math. Pura Appl. (Ser. 4A) 83, 261‒335.