On Chen immersions into Lorentzian space forms with nonflat normal space

Dursun U.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.57, pp.375-387, 2000 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 57
  • Publication Date: 2000
  • Page Numbers: pp.375-387


Let f : M-m --> (M) over tilde (m+2)(1) (c) be a smooth totally geodesic isometric immersion from an m-dimensional connected Riemannian manifold M-m into an (m+2)-dimensional Lorentzian space form (M) over tilde (m+2)(1) (c). Let xi be a nonparallel time-like normal vector field on Mm. By using the normal exponential map we define, for some t epsilon R, a push-out map ft(x) = exp(x, t xi (x)) into the Lorentzian space form (M) over tilde1, where x epsilon M. We show that the map ft is a nontrivial Chen immersion with nonflat normal bundle under some conditions on the components of the normal connection form. We construct some examples.