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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

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