Totally contact umbilical screen-slant and screen-transversal lightlike submanifolds of indefinite Kenmotsu manifold

Abstract

We study totally contact umbilical screen-slant lightlike submanifolds and totally contact umbilical screen-transversal lightlike submanifolds of an indefinite Kenmotsu manifold. We prove a characterization theorem of totally contact umbilical screen-slant lightlike submanifolds of an indefinite Kenmotsu manifold. We further prove some results on a totally contact umbilical radical screen-transversal lightlike submanifold of an indefinite Kenmotsu manifold, such as the necessary and sufficient conditions for the screen distribution $S(TM)$ to be integrable and for the induced connection $\nabla$ to be a metric connection.

Keywords

• indefinite kenmotsu manifold
• lightlike submanifold
• totally contact umbilical screen-slant lightlike submanifold
• totally contact umbilical radical screen-transversal lightlike submanifold