Intrinsic Geometric Flows on Manifolds of Revolution

An intrinsic geometric flow is an evolution of a Riemannian metric by a two-tensor. An extrinsic geometric flow is an evolution of an immersion of a manifold into Euclidean space. An extrinsic flow induces an evolution of a metric because any immersed manifold inherits a Riemannian metric from Euclidean space. In this paper we discuss the inverse problem of specifying an evolution of a metric and then seeking an extrinsic geometric flow which induces the given metric evolution. We limit our discussion to the case of manifolds that are rotationally symmetric and embeddable with codimension one. In this case, we reduce an intrinsic geometric flow to a plane curve evolution. In the specific cases we study, we are able to further simplify the evolution to an evolution of a function of one variable. We provide soliton equations and give proofs that some soliton metrics exist.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

The University of Arizona.

Year dc:date.issued

2010

Author dc:creator

• Taft, Jefferson

Advisor dc:contributor.advisor

• Glickenstein, David

Committee members dc:contributor.committeemember

• Glickenstein, David
• Friedlander, Leonid
• Pickrell, Douglas
• Venkataramani, Shankar

• Differential Geometry
• Geometric Flow
• Ricci Flow
• Yamabe Flow

Statement dc:rights

• Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10150/194925

OAI identifier oai:identifier

oai:repository.arizona.edu:10150/194925