Minimal immersions of 2-manifolds into spheres (Q796131)

The following theorem is proved. Let \(M^ 2\) be a compact, connected, two-dimensional Riemannian manifold with curvature K. Assume that 1/6\(\leq K\leq 1/3\), and let \(x:M^ 2\to S^ N(1)\) be an isometric minimal immersion into the unit N-sphere. Then either \(K=1/3\) or \(K=1/6\), and the immersions are the standard minimal immersions corresponding to the spherical harmonics of order 2 and 3. The proof depends on finding a suitable integral formula.