Stredder, Peter Jeremy (1976) Vector and tensor fields. PhD thesis, University of Warwick.

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Abstract

This thesis consists of two unconnected parts. In the first part we study the Cr-conjugacy classes of flows on two dimensional manifolds whose flow lines near a fixed point are diffeomorphic to the level surfaces of a Morse function near a critical point and which have no holonomy. We show how these can be decomposed into those in which every flow line is closed and those in which no flow line is closed. In the remainder of the thesis we consider the latter case and show that then the number of limit sets is finite. He describe their geometry and use the techniques of ergodic theory to show that the number of asymptotic cycles is finite in certain cases. We show that the asymptotic cycles are classifying for flow of this type on a manifold of genus 2 with exactly two non- trivial limit sets. Finally we give some new examples on manifolds of higher genus both of flows in which every flow line is [] and of flows in which each limit set is a closed, nowhere dense set which meets any transverse interval in a perfect set.

In the second part we consider differential operators which are functionally associated to Hiemannian manifolds and which satisfy a regularity condition that arise in the proof of the index theorem via the heat equation. These are classified in terms of the On-equivariant representations of the general linear group.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Vector fields, Tensor fields
Official Date:	1976
Dates:	Date Event 1976 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Epstein, D. B. A.
Extent:	235 leaves
Language:	eng

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