Opozda, Barbara 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 Keywords:minimal submanifold; totally real submanifold; totally geodesic Citations:Zbl 0627.00012 × Cite Format Result Cite Review PDF Full Text: EuDML