An example of rotational hypersurface in Rⁿ⁺¹ with induced IP metric from Rⁿ⁺¹

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.

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