On hypersurfaces with constant mean curvature in hyperbolic space (Q1378317)

\textit{K. Nomizu} and \textit{B. Smyth} [J. Differ. Geom. 3, 367-377 (1969; Zbl 0196.25103)] derived a new Simons' type formula for the Laplacian of the square of the second fundamental form of a submanifold immersed with constant mean curvature in a space of constant sectional curvature and determined the hypersurfaces \(M\) of non-negative sectional curvature immersed in \(\mathbb{R}^{n+1}\) or \(S^{n+1}\). \textit{M. Okumura} [Am. J. Math. 96, 207-213 (1974; Zbl 0302.53028)] considered this problem substituting the condition on the non-negativity of the sectional curvature of \(M\) with a pinching condition on the second fundamental form. In this paper, the author gives some new results on the hypersurfaces of constant mean curvature of hyperbolic space with pinching conditions on the principal curvatures.