Minimal immersions of surfaces into 4-dimensional space forms (Q1063266)

The authors find a necessary and sufficient condition for a real valued function on a simply connected surface M to be the normal curvature function of a minimal immersion into a 4-dimensional space of constant curvature c. As a corollary they obtain characterizations of the Veronese surface in \(S^ 4\) and the Clifford torus in \(S^ 3\subset S^ 4\) by certain inequalities for the normal curvature. Also they study deformations of minimal surfaces preserving the normal curvature.