On geometry of pointwise slant lightlike submersions with totally umbilical fibers

We define notion of a pointwise slant lightlike submersion from an indefinite almost Hermitian manifold (M1,g1,J)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(M_{1}, g_{1}, J)$$\end{document}, where g1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{1}$$\end{document} is a semi-Riemannian metric of index 2r, onto an r-lightlike manifold and discuss for its existence. We also obtain some conditions for a pointwise slant lightlike submersion to be a slant lightlike submersion. Finally, we study pointwise slant lightlike submersions with totally umbilical fibers and show that such submersions to have only totally geodesic fibers.