Let X be a relatively compact
complex subspace of a hermitian manifold N with hermitian distance dN. Let Ω be a
bounded domain with C1-boundary in Cm. A holomorphic mapping f : Ω → N,
f(Ω) ⊂ X, is called a normal mapping if the family {f ∘ ψ : ψ : Δ → Ω is
holomorphic}, Δ := {z ∈ C : |z| < 1}, is a normal family in the sense of H. Wu. Let
{pn} be a sequence of points in Ω which tends to a boundary point ζ ∈ ∂Ω
such that limn→∞dN(f(pn),l) = 0 for some l ∈X. Two sets of sufficient
conditions on {pn} are given for a normal mapping f : Ω → X to have the
non-tangential limit value l, thus extending the results obtained by Bagemihl and
Seidel.
