Existence and uniqueness theorems for pointwise slant immersions in complex space forms

Abstract

An isometric immersion f : Mn ? ?Mm from an n-dimensional Riemannian manifold Mn into an almost Hermitian manifold ?Mm of complex dimension m is called pointwise slant if its Wirtinger angles define a function defined on Mn. In this paper we establish the Existence and Uniqueness Theorems for pointwise slant immersions of Riemannian manifolds Mn into a complex space form ?Mn(c) of constant holomorphic sectional curvature c, which extend the Existence and Uniqueness Theorems for slant immersions proved by B.-Y. Chen and L. Vrancken in 1997.