Persistent Link:
http://hdl.handle.net/10150/194925
Title:
Intrinsic Geometric Flows on Manifolds of Revolution
Author:
Taft, Jefferson
Issue Date:
2010
Publisher:
The University of Arizona.
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.
Abstract:
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.
Type:
text; Electronic Dissertation
Keywords:
Differential Geometry; Geometric Flow; Ricci Flow; Yamabe Flow
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Glickenstein, David
Committee Chair:
Glickenstein, David

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleIntrinsic Geometric Flows on Manifolds of Revolutionen_US
dc.creatorTaft, Jeffersonen_US
dc.contributor.authorTaft, Jeffersonen_US
dc.date.issued2010en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © 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.en_US
dc.description.abstractAn 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.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectDifferential Geometryen_US
dc.subjectGeometric Flowen_US
dc.subjectRicci Flowen_US
dc.subjectYamabe Flowen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorGlickenstein, Daviden_US
dc.contributor.chairGlickenstein, Daviden_US
dc.contributor.committeememberGlickenstein, Daviden_US
dc.contributor.committeememberFriedlander, Leoniden_US
dc.contributor.committeememberPickrell, Douglasen_US
dc.contributor.committeememberVenkataramani, Shankaren_US
dc.identifier.proquest11225en_US
dc.identifier.oclc752261069en_US
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