Geometry of Riemannian Maps from Generic Submanifolds of Kähler Manifolds

This paper extends the theory of Riemannian maps to the setting of generic submanifolds of Kähler manifolds. We introduce the notion of holomorphic Riemannian maps from generic submanifolds and establish fundamental relations between the geometric structures involved. Our main results include a characterization of when the image distribution inherits a Kähler structure, a harmonicity criterion for such maps, and a relation between holomorphic sectional curvatures. The theory developed here generalizes previous work on CR-submanifolds while demonstrating new phenomena specific to the generic case. Several explicit examples illustrate the non-trivial nature of our results.