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The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms. (English) Zbl 0997.53006
The paper contains the following new result: If a surface in $\bbfC\bbfP^2 (4\rho)$ (= the complex projective plane endowed with the Fubini-Study metric of constant holomorphic sectional curvature $4\rho)$ has parallel mean curvature vector, then it is minimal or has constant Gaussian curvature. A new class of surfaces (in $\bbfC^2$ and $\bbfC\bbfH^2 (-4))$ with parallel mean curvature vector which are not of constant Kähler angle are found.
Reviewer: A.Neagu (Iaşi)

53A10Minimal surfaces, surfaces with prescribed mean curvature
49Q05Minimal surfaces (calculus of variations)
53C56Other complex differential geometry
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