Erhan Güler

The Gauss Map and the Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space

Erhan Güler Bartın University Faculty of Sciences Department of Mathematics 74100, Bartın Turkey; eguler@bartin.edu.tr * Correspondence: eguler@bartin.edu.tr; Tel.: +90-378-5011000-1553 Academic Editor: name Version June 11, 2018 submitted to Preprints Abstract: We consider rotational hypersurface in the four dimensional Euclidean space. We calculate 1 the mean curvature and the Gaussian curvature, and some relations of the rotational hypersurface. 2 Moreover, we define the third Laplace-Beltrami operator and apply it to the rotational hypersurface. 3

Helicoidal Hypersurfaces of Dini-Type with Spacelike Axis in Minkowski 4-Space

In this paper, we define Ulisse Dini-type helicoidal hypersurface with spacelike axis in 1 Minkowski 4-space E1. We compute the Gaussian and the mean curvature of the hypersurface. 2 Moreover, we obtain some special symmetry to the curvatures when they are flat and maximal. 3