{"id":{"repo_id":"arizona-thes","oai_identifier":"oai:repository.arizona.edu:10150/194925"},"canonical_url":"https://search.dev.ndltd.org/etd/arizona-thes/oai:repository.arizona.edu:10150/194925","repository":{"repo_id":"arizona-thes","name":"University of Arizona","base_url":"https://repository.arizona.edu/oai/request"},"display":{"title":"Intrinsic Geometric Flows on Manifolds of Revolution","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Taft, Jefferson"],"institution":"The University of Arizona.","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Glickenstein, David"],"committee_chairs":[],"committee_members":["Glickenstein, David","Friedlander, Leonid","Pickrell, Douglas","Venkataramani, Shankar"],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-24T00:57:22Z","subjects":["Differential Geometry","Geometric Flow","Ricci Flow","Yamabe Flow"],"languages":["en"],"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."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10150/194925","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Glickenstein, David"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Glickenstein, David","Friedlander, Leonid","Pickrell, Douglas","Venkataramani, Shankar"]},{"key":"dc:creator","label":"Author","values":["Taft, Jefferson"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2011-12-06T13:30:26Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-12-06T13:30:26Z"]},{"key":"dc:date.issued","label":"Date","values":["2010"]},{"key":"dc:publisher","label":"Institution","values":["The University of Arizona."]},{"key":"dc:type","label":"Dc Type","values":["text","Electronic Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics","Graduate College"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Arizona"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Differential Geometry","Geometric Flow","Ricci Flow","Yamabe Flow"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["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."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10150/194925"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Intrinsic Geometric Flows on Manifolds of Revolution"]}]}],"canonical_facts":{"dc:contributor.advisor":["Glickenstein, David"],"dc:contributor.committeemember":["Glickenstein, David","Friedlander, Leonid","Pickrell, Douglas","Venkataramani, Shankar"],"dc:creator":["Taft, Jefferson"],"dc:date.accessioned":["2011-12-06T13:30:26Z"],"dc:date.available":["2011-12-06T13:30:26Z"],"dc:date.issued":["2010"],"dc:description.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."],"dc:identifier.uri":["http://hdl.handle.net/10150/194925"],"dc:language.iso":["en"],"dc:publisher":["The University of Arizona."],"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."],"dc:subject":["Differential Geometry","Geometric Flow","Ricci Flow","Yamabe Flow"],"dc:title":["Intrinsic Geometric Flows on Manifolds of Revolution"],"dc:type":["text","Electronic Dissertation"],"thesis:degree_discipline":["Mathematics","Graduate College"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Arizona"]},"updated_at":"2026-07-24T00:57:22Z"}