Examples of minimal unit vector fields
The main purpose of the paper under review is to present a series of examples of Riemannian manifolds equipped with a minimal unit vector field. These examples belong to the following classes of Riemannian manifolds: \(2\)-dimensional manifolds; \(3\)-dimensional manifolds; semi-direct products \(\mathbb{R} \times _{\alpha} \mathbb{R}\), where \(\alpha : \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}\) is a linear map; warped products \(\mathbb{R} \times _{f} M\) of the one-dimensional Euclidean space \(\mathbb{R}\) and the \(n\)-dimensional Riemannian manifold; doubly warped products \(\mathbb{R} \times _{f} M_{1} \times _{g} M_{2}\), K-contact manifolds; contact metric \((k,\mu)\)-spaces; Kenmotsu manifolds; the generalized Heisenberg groups \(H(1,r)\) (introduced by Y. Haraguchi); generalized Heisenberg groups (introduced by A. Kaplan) and the Damek-Ricci spaces. Let us mention that the Damek-Ricci spaces provided the first class of examples of harmonic spaces which are not locally symmetric.
strongly normal and minimal vector fields
scientific article; zbMATH DE number 1530059