A contact Riemannian manifold whose Reeb vector field is harmonic is called H-contact manifold. The aim of this paper, based on the lecture given by the author at the Università della Basilicata in April 2004, is to review some results related to the geometry of a H-contact manifold. The content is the following: Sect.2 Harmonicity of unit vector fields. Sect.3 Harmonicity of the Reeb vector field. Sect.4 Three-dimensional H-contact manifolds. Sect.5 The energy of a unit vector fied and the Chern-Hamilton energy. Sect.6 Harmonicity of Hopf vector fields of real hypersurfaces in Kaehler manifolds. Sect.7 Real hypersurfaces of contact type. Sect.8 Some questions.
Geometry of contact Riemannian manifolds whose Reeb vector field is harmonic
PERRONE, Domenico
2005-01-01
Abstract
A contact Riemannian manifold whose Reeb vector field is harmonic is called H-contact manifold. The aim of this paper, based on the lecture given by the author at the Università della Basilicata in April 2004, is to review some results related to the geometry of a H-contact manifold. The content is the following: Sect.2 Harmonicity of unit vector fields. Sect.3 Harmonicity of the Reeb vector field. Sect.4 Three-dimensional H-contact manifolds. Sect.5 The energy of a unit vector fied and the Chern-Hamilton energy. Sect.6 Harmonicity of Hopf vector fields of real hypersurfaces in Kaehler manifolds. Sect.7 Real hypersurfaces of contact type. Sect.8 Some questions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
