Every manifold admits a nowhere vanishing complex vector field. If, however, the manifold is compact and orientable and the complex bilinear form associated to a Riemannian metric is never zero when evaluated on the vector field, then the manifold must have zero Euler characteristic. One of the oldest and most basic results in global differential topology… (More)
T he theory of functions (what we now call the theory of functions of a complex variable) was one of the great achievements of nineteenth century mathematics. Its beauty and range of applications were immense and immediate. The desire to generalize to higher dimensions must have been correspondingly irresistible. In this desire to generalize, there were two… (More)
The optimal dimensions N are determined so that each smooth manifold of dimension n admits a totally real immersion or an independent map to C N. Detailed results comparing these two optimal dimensions, as well as some related results, are presented for four-manifolds.
We study the interrelation among pseudohermitian and Lorentzian geometry as prompted by the existence of the Fef-ferman metric. Specifically for any nondegenerate CR manifold M we build its b-boundary ˙ M. This arises as a S 1 quotient of the b-boundary of the (total space of the canonical circle bundle over M endowed with the) Fefferman metric. Points of ˙… (More)
Geometric sensitivity for single photon emission computerized tomography (SPECT) is given by a double integral over the detection plane. It would be useful to be able to explicitly evaluate this quantity. This paper shows that the inner integral can be evaluated in the situation where there is no gamma ray penetration of the material surrounding the pinhole… (More)