‎We prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite Sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎We also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite Sasakian space forms‎.

In this paper is studied the behavior of principal curvature lines near a curve of umbilic points of a smooth surface.

We investigate the twistor space and the Grassmannian fibre bundle of a Lorentzian 4-space with natural almost optical structures and its induced CR-structures. The twistor spaces of the Lorentzian space forms R 4 1, S 4 1 and H 4 1 are explicitly discussed. The given twistor construction is applied to surface theory in Lorentzian 4-spaces. Immersed spacelike surfaces in a Lorentzian 4-space wi...

One purpose of this article is to draw attention to the seminal work of J. Mealy in 1989 on calibrations in semi-riemannian geometry where split SLAG geometry was first introduced. The natural setting is provided by doing geometry with the complex numbers C replaced by the double numbers D, where i with i = −1 is replaced by τ with τ = 1. A rather surprising amount of complex geometry carries o...

In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite pa...