No abstract

We consider the difference tensor field of the Levi-Civita connections of the first and third fundamental form for non-degenerate hypersurface immersions in space forms. Within this framework, we characterize quadrics in terms of their principal curvature functions.

We classify the hypersurfaces of space forms for which the cubic form is divisible by the metric (g|C). In other words, when does the symmetric traceless part of the cubic form vanish, where the trace is taken with respect to the first fundamental form?Mathematics Subject Classification (2000). 53B25, 53A07.