Let f: be an isometric immersion from a Riemannian manifold N into an almost Hermitian manifold M. For each non-zero tangent vector X in at the Wirtinger angle is defined as the angle between and , where J is the almost complex structure on M. If (X) is of constant value for all non-zero tangent vectors X to N, then f is called a slant immersion characterizes the holomorphic and anti- holomorphic immersions into M). In case 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 . Besides some characterizations of such surfaces he gives several (non-trivial) examples and obtains a classification of slant surfaces in with parallel mean curvature vector. [Reviewer’s remark: Recently, the author and Y. Tazawa proved that every compact slant submanifold in is totally real [Slant submanifolds in complex number spaces (preprint)].]