We introduce screen transversal lightlike submanifolds of golden semi-Riemannian manifolds, then we define its subclasses (radical screen transversal, screen transversal anti-invariant lightlike submanifolds). We find the condition of integrability of distribution which are involved in the definition of radical screen transversal lightlike submanifolds of golden semi-Riemannian manifolds, we investigate the geometry of leaves of distributions. We obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study these submanifolds under condition to be totally umbilical and give an example of such submanifolds. We show that if M is a totally umbilical radical screen transversal lightlike submanifold of a golden semi-Riemannian manifold, then the screen distribution and the radical distribution are always integrable and the screen distribution always defines a totally geodesic foliation. Moreover, we investigate several properties of screen transversal anti-invariant lightlike submanifolds of golden semi-Riemannian manifolds and obtain some geometric results. We give some equivalent conditions for integrability of distributions and investigate the geometry of leaves of distributions. We find a theorem which shows that the induced connection is a metric connection under some conditions. We also study the geometry of totally umbilical screen transversal anti-invariant lightlike submanifolds and give an example.
Anahtar Kelimeler: Golden Semi-Riemannian Manifolds, Golden Structure, Lightlike Submanifolds, Screen Transversal Lightlike Submanifolds