A New Pinching for Closed 3-dimensional Hypersurfaces

S. C. de Almeida, F. G. B. Brito, M. Scherfner, S. Weiss

We will give a new pinching for closed oriented 3-dimensional hypersurfaces immersed in a not necessarily complete space of constant curvature, where we always assume that the hypersurfaces have constant mean curvature $H$ and constant scalar curvature $\kappa$. The given assumptions indicate that our result touches the setting of the Chern conjecture for isoparametric hypersurfaces in spheres.