On the Chern Forms of Kaehler Hypersurfaces in Complex Space Forms.
Let be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by to have degenerate -transform or -transform are given.
In this paper we obtain a lower bound for the first Dirichlet eigenvalue of complete spacelike hypersurfaces in Lorentzian space in terms of mean curvature and the square length of the second fundamental form. This estimate is sharp for totally umbilical hyperbolic spaces in Lorentzian space. We also get a sufficient condition for spacelike hypersurface to have zero first eigenvalue.
In this note we show that -scrolls over null curves in a 3-dimensional Lorentzian space form are characterized as the only ruled surfaces with null rulings whose Gauss maps satisfy the condition , being a parallel endomorphism of .