Isotropic Totally Real Submanifolds.
We study lightlike hypersurfaces of an indefinite Kaehler manifold of quasi-constant curvature subject to the condition that the characteristic vector field of is tangent to . First, we provide a new result for such a lightlike hypersurface. Next, we investigate such a lightlike hypersurface of such that (1) the screen distribution is totally umbilical or (2) is screen conformal.
We use reflections with respect to submanifolds and related geometric results to develop, inspired by the work of Ferus and other authors, in a unified way a local theory of extrinsic symmetric immersions and submanifolds in a general analytic Riemannian manifold and in locally symmetric spaces. In particular we treat the case of real and complex space forms and study additional relations with holomorphic and symplectic reflections when the ambient space is almost Hermitian. The global case is also...