Relative nullity foliations and indefinite isometric immersions
This paper investigates the relative nullity distribution of an indefinite Riemannian manifold isometrically immersed into an indefinite space form. This distribution is totally geodesic, and gives rise to a Riccati-type differential equation along a geodesic in a leaf of the distribution. This differential equation is applied in several ways to estimate the index of relative nullity for geodesically complete, connected, Lorentzian submanifolds of codimension one in the Lorentzian space forms of constant positive curvature. These applications extend work of Abe, Ferus, and others to the setting of indefinite metrics.
scientific article; zbMATH DE number 3975797