Foliations of the Sasakian space \({\mathbb R}^{2n+1}\) by minimal slant submanifolds (Q1964625)

An immersed submanifold \(N\) of an almost contact metric manifold \(M\) with structure \((\phi,\xi,\eta,g)\), is called slant if, for any \(x\in N\), the angle \(\vartheta(X)\) between \(\phi X\) and \(T_xN\), where \(X\in T_x N\) is linearly independent of \(\xi_x\), is a constant that does not depend on the choice of \(x\) and \(X\). In the present paper, the author gives non-trivial examples of slant submanifolds of \({\mathbb R}^{2n+1}\) endowed with the standard Sasakian structure. It is proved that \({\mathbb R}^{2n+1}\) admits a harmonic Riemannian 3-dimensional foliation whose leaves are all slant submanifolds with prescribed angle \(\vartheta\). Moreover, the author describes some useful facts about the intrinsic geometry of the leaves of this foliation, such as their local homogeneity and an interesting algebraic property of the Ricci tensor.