Rotation Hypersurfaces With Constant Scalar Curvature In S~n×R

In this paper, we study the rotation hypersurfaces in Sn×R. Our main results are as follows:(1) we calculate some fundamental quantities such as connection forms, mean curvature, the square of the length of the second fundamental form, the Laplacian of the mean curvature and scalar curvature of rotation hypersurfaces with respect to a certain frame.(2) we summarize some results about hypersurfaces and rotation hypersurfaces in Sn×R studied by many geometers.(3) we study the rotation hypersurfaces with one constant principal curvature,two constant principal curvatures and two principal curvatures but one of which is constant in Sn×R. Moreover, we classify these hypersurfaces.(4) we find a necessary and su?cient condition for a rotation hypersurface in Sn×R having constant mean curvature and constant scalar curvature.(5) we give a classification for rotation hypersurfaces with constant scalar curvature R = n(n- 1).