Characteristic Lightlike Submanifolds of an IndefiniteS-Manifold

We study characteristicr-lightlike submanifoldsMtangent to the characteristic vector fields in an indefinite metricS-manifold, and we also discuss the existence of characteristic lightlike submanifolds of an indefiniteS-space form under suitable hypotheses: (1)Mis totally umbilical or (2) its screen distributionS(TM)is totally umbilical inM.

Harmonic characteristic vector fields on contact metric three-manifolds

In this paper we show that a contact metric three-manifold is a generalised (k, μ)-space on an everywhere dense open subset if and only if its characteristic vector field ξ determines a harmonic map from the manifold into its unit tangent sphere bundle equipped with the Sasaki metric. Moreover, we classify the contact metric three-manifolds whose characteristic vector field ξ is strongly normal (or equivalently, is harmonic and minimal).