Two characterization theorems for irrotational lightlike geometry (Q2868492)

In the last \(15\) years light-like submanifolds raised the interest of a number of mathematicians. So the theme in the present paper can be said modern enough. The results obtained have sufficient weight. The author has introduced half light-like submanifolds of a semi-Riemannian spaceform with a semi-symmetric non-metric connection. At first it is proved that if \(M\) is an irrotational screen quasi-conformal half light-like submanifold of a semi-Riemannian spaceform \(\tilde M(c)\) admitting a non-symmetric non-metric connection whose structure vector field \(\xi\) is tangent to \(M\), but it does not belong to \(\mathrm{S}(TM)\), then \(c=1\).NEWLINENEWLINENEWLINEAlso it is proved that if \(M\) is screen conformal, then \(c=0\). Finally, it is remarked that screen conformal and screen quasi-conformal of \(M\) are mutually independent to each other.