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

Abstract

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