Communications of the
Korean Mathematical Society CKMS

We study totally umbilical real half lightlike submanifolds of indefinite Kaehler manifolds with a quarter-symmetric metric connection. We obtain some conditions for a real half lightlike submanifold of an indefinite Kaehler manifold with a quarter-symmetric metric connection to be a product manifold. We derive the expression for induced Ricci type tensor $\mathcal{R}^{(0, 2)}$ and also obtain conditions for $\mathcal{R}^{(0, 2)}$ to be symmetric.

Keywords: Indefinite Kaehler manifold, real half lightlike submanifolds, quarter-symmetric metric connection, null sectional curvature, induced Ricci type tensor

MSC numbers: Primary 53B15, 53C40, 53C50