Immersions of Lorentzian submanifolds into R1m with pointwise 2-planar sections and on the circles and pseudo spheres in Lorentzian geometry

Abstract

We planned this paper into two main sections. In the first section, we gjve an analog for the Lorentzian case of some characterizations given in [2 ]. There is no difference between the characterizations in both cases of inunersions with (pointwise) 2-planar normal sections of Riemannian and Lorentzian manifolds into R™ and R,”*, respectively, but the ptoofs. In the second part of paper, we deal with the Tlıeorem. 3.2 given in [1 ] and show that there must be some extra hypothesis to get the characterizations given as Theorems 2.1 and 2.2 in the present paper.