On the linear vector fields in E2n+1

Authors : Abolfazl ACRATALISHIAN

Pages : 0-0

Doi:10.1501/Commua1_0000000532

View : 8 | Download : 8

Publication Date : 1990-01-01

Article Type : Research Paper

Abstract :Karger and Novak [1 ] has shown that the integral curves of a linear vector field X on E3 which has a matrix “ A C~ are: _ 0 1 _ insert ignore into journalissuearticles values(i); . Helices with common axes and the same parameter if rank [AC] — 3, insert ignore into journalissuearticles values(ii); . Circles which lie on planes parallel to each other, and which have centers on the axis per- pendicular to those parallel planes, if rank [AC] = 2, insert ignore into journalissuearticles values(iii); .Parallel straight lines, if rank [AC] = 1. In this study, the results of Karger and Novak are extended to E2n+1 where n > l. It is shown that of ali the results are also valid in this general case and some further elaborations are included.
Keywords : Karger, Novak, vector