We introduce radical anti-invariant lightlike submanifolds of a semi Riemannian product manifold and give examples. After we obtain the conditions of integrability of distributions which are involved in the definition of radical anti-invariant lightlike submanifolds, we investigate the geometry of leaves of distributions. We also obtain the induced connection is a metric connection and a radical anti-invariant lightlike submanifold is a product manifold under certain conditions. Finally, we study totally umbilical radical anti-invariant lightlike submanifolds and observe that they are totally geodesic under a condition.
KILIÇ, EROL and ŞAHİN, BAYRAM (2008) "Radical Anti-Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds," Turkish Journal of Mathematics: Vol. 32: No. 4, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol32/iss4/5