*(English)*Zbl 0677.53060

Let f: $N\to M$ be an isometric immersion from a Riemannian manifold N into an almost Hermitian manifold M. For each non-zero tangent vector X in ${T}_{p}N$ at $p\in N$ the Wirtinger angle $\theta \left(X\right)\in [0,\pi /2]$ is defined as the angle between $J{f}_{*}X$ and ${f}_{*}{T}_{p}N$, where J is the almost complex structure on M. If $\theta $ (X) is of constant value $\theta \ne 0$ for all non-zero tangent vectors X to N, then f is called a slant immersion $(\theta =0$ characterizes the holomorphic and anti- holomorphic immersions into M). In case $\theta =\pi /2$ the immersion f is also called totally real.

At first the author proves some fundamental properties of slant immersions. Then he restricts to the special case of slant surfaces in the complex 2-plane ${\u2102}^{2}$. Besides some characterizations of such surfaces he gives several (non-trivial) examples and obtains a classification of slant surfaces in ${\u2102}^{2}$ with parallel mean curvature vector. [Reviewerâ€™s remark: Recently, the author and *Y. Tazawa* proved that every compact slant submanifold in ${\u2102}^{m}$ is totally real [Slant submanifolds in complex number spaces (preprint)].]