On semi-invariant $\xi^{\perp}$-submanifolds of Lorentzian para-Sasakian manifolds

Abstract

In the present paper, we study semi-invariant $\xi^{\perp}$-submanifolds of Lorentzian para-Sasakian manifolds. We find the the integrability conditions of distributions on semi-invariant $\xi^{\perp}$-submanifolds of Lorentzian para-Sasakian manifolds. We also obtain some characterizations for the totally umbilical semi-invariant $\xi^{\perp}$-submanifolds of Lorentzian para-Sasakian manifolds.