C-totally real submanifolds of Sasakian space forms
On an odd-dimensional unit sphere \(S^{2n+1}(1)\) one can define a Sasakian structure in a natural way. In this paper we prove that, if the sectional curvatures \(K\) of an \(n\)-dimensional, compact, minimal, C-totally real submanifold \(M^n\) of \(S^{2n+1}(1)\) satisfy \(0\leq K\leq 1\), then either \(K\equiv 1\) \((M^n\) is totally geodesic) or \(K\equiv 0\) \((M^n\) is flat). Finally we give examples of submanifolds satisfying \(K\equiv 0\) and \(K\equiv 1\), as well as an example showing that the upper bound \(K\leq 1\) is needed.
scientific article; zbMATH DE number 4067813