Minimal surfaces with low index in the three-dimensional sphere. (English) Zbl 0691.53049
The author obtains the following result: Let M be a compact orientable non-totally-geodesic minimal surface in the three-dimensional unit sphere \(S^ 3(1)\). Then ind(M)\(\geq 5\), and the equality holds if and only if M is the Clifford torus, where ind(M) is the index of the Jacobi operator of M in \(S^ 3(1)\).
Reviewer: T.Ishihara
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
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