Normalization and prescribed extrinsic scalar curvature on lightlike hypersurfaces - ATINDOGBE, COMLAN CYRIAQUE (My University, 2010)
In a recent paper [C. Atindogbé, Scalar curvature on lightlike hypersurfaces, Appl. Sci. 11 (2009) 9–18], the present author considered the concept of extrinsic (induced) scalar curvature on lightlike hypersurfaces. This scalar quantity has been studied on lightlike hypersurfaces equipped with a given normalization. But a very important problem was left open: How to characterize the set of all normalizations admitting a prescribed extrinsic scalar curvature? In this paper, we provide various responses to this question, supported by examples.
Keywords: Lightlike hypersurface; Normalization; Extrinsic scalar curvature