Reduction of the codimension for lightlike isotropic submanifolds

✍ Scribed by Cyriaque Atindogbe; Jean-Pierre Ezin; Joël Tossa

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 78 KB
• Volume: 42
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(01)00027-4

✦ Synopsis

We give a sufficient condition for a lightlike isotropic submanifold M, of dimension n, which is not totally geodesic in a semi-Riemannian manifold of constant curvature c and of dimension n + p(n < p), to admit a reduction of codimension. We show that this condition is a necessary and sufficient condition on the first transversal space of M. There are basic and non-trivial differences from the Riemannian case, as developed by Dajczer et al.