Ruling euclidean 3 -space.

Title: Ruling euclidean 3 -space.
Identifier: AAI9969734
identifier: 9969734
Creator: Siegel, Evan John.
Contributor: Adviser: John Velling
Date: 2000
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: This essay studies Cr foliations of R3 by lines, or rulings of R 3. In addition to rulings of R3, by (1) parallel lines and (2) lines which lie in parallel planes which themselves foliate R3 there are rulings by (3) a skew set of lines. Rulings of the third type have a "flexibility." The Jacobian of the Gauss map of the leaves in the foliation is studied. Flow along leaves between transverse planes preserves area if and only if the determinant of this Jacobian vanishes. Connected sets of parallel leaves must be convex. The set of leaves parallel to a given leaf can have no more than two connected components. These components can either be a pair of coplanar half-planes or they are on opposite sides of a pair of asymptotic planes.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.