AN EXAMPLE OF ROTATIONAL HYPERSURFACE IN $\mathbb{R}^{n+1}$ WITH INDUCED IP METRIC FROM $\mathbb{R}^{n+1}$

Abstract

We find a rotated hypersurface Mⁿ whose induced metric from Rⁿ⁺¹ is isometric to metric of IP manifolds and therefore the hypersurface is conformally flat. In the case of 4-dimensional hypersurface with IP metric we have presented explicitly a skew-symmetric curvature operator and have proved directly that its eigenvalues are pointwise. We find the mean curvature of the hypersurface.