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Totally real submanifolds of \(S^ 6(1)\) with parallel second fundamental form. (English) Zbl 0635.53025

Abstract analysis, Proc. 14th Winter Sch., SrnĂ®/Czech. 1986, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 14, 247-253 (1987).
[For the entire collection see Zbl 0627.00012.]
Let M be a totally real submanifold of the six-dimensional Euclidean sphere \(S^ 6(1)\). The author proves: (i) if dim M\(=3\), then M is totally geodesic, (ii) if dim M\(=2\) and M is minimal, then M is either totally geodesic or locally flat.
Reviewer: A.Bejancu

MSC:

53C40 Global submanifolds

Citations:

Zbl 0627.00012