Showing papers by "David E. Blair published in 1995"
TL;DR: In this article, a study of contact metric manifolds for which the characteristic vector field of the contact structure satisfies a nullity type condition, condition (*) below, is presented.
Abstract: This paper presents a study of contact metric manifolds for which the characteristic vector field of the contact structure satisfies a nullity type condition, condition (*) below. There are a number of reasons for studying this condition and results concerning it given in the paper: There exist examples in all dimensions; the condition is invariant underD-homothetic deformations; in dimensions>5 the condition determines the curvature completely; and in dimension 3 a complete, classification is given, in particular these include the 3-dimensional unimodular Lie groups with a left invariant metric.
325 citations
TL;DR: In this article, it was shown that if a 3-dimensional submanifold is invariant with respect to one of the Sasakian structures and invariant to another, then it is a principal circle bundle over a holmophic Legendre curve in complex projective 3-space.
Abstract: A sphere of dimension 4n+3 admits three Sasakian structures and it is natural to ask if a submanifold can be an integral submanifold for more than one of the contact structures. In the 7-sphere it is possible to have curves which are Legendre curves for all three contact structures and there are 2 and 3-dimensional submanifolds which are integral submanifolds of two of the contact structures. One of the results here is that if a 3-dimensional submanifold is an integral submanifold of one of the Sasakian structures and invariant with respect to another, it is an integral submanifold of the remaining structure and is a principal circle bundle over a holmophic Legendre curve in complex projective 3-space.
7 citations