CHAPTER II - INTEGRAL TRANSFORMS IN THE COMPLEX DOMAIN

Abstract

This chapter focuses on some problems of integral geometry in the complex domain. The equation p = ‘α, z’ implies that the line is uniquely determined by its Plucker coordinates. Conversely, the Plucker coordinates are determined uniquely by the line to within a constant factor. The set of all lines in a three-dimensional complex space can be considered a manifold. The set of numbers (α1, α2, α3, p1, p2, p3) are assumed to be homogeneous coordinates of points in a five-dimensional complex projective space. These will be the Plucker coordinates of a line if and only if (α, p) = 0.