Geometry of Spaces of Planar Quadrilaterals

Simple item page
dc.contributor.authorStClair, Jessica Lindseyen
dc.contributor.committeechairHaskell, Peter E.en
dc.contributor.committeememberDay, Martin V.en
dc.contributor.committeememberFloyd, William J.en
dc.contributor.committeememberThomson, James E.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:09:42Zen
dc.date.adate2011-05-04en
dc.date.available2014-03-14T20:09:42Zen
dc.date.issued2011-04-14en
dc.date.rdate2011-05-04en
dc.date.sdate2011-04-15en
dc.description.abstractThe purpose of this dissertation is to investigate the geometry of spaces of planar quadrilaterals. The topology of moduli spaces of planar quadrilaterals (the set of all distinct planar quadrilaterals with fixed side lengths) has been well-studied [5], [8], [10]. The symplectic geometry of these spaces has been studied by Kapovich and Millson [6], but the Riemannian geometry of these spaces has not been thoroughly examined. We study paths in the moduli space and the pre-moduli space. We compare intraplanar paths between points in the moduli space to extraplanar paths between those same points. We give conditions on side lengths to guarantee that intraplanar motion is shorter between some points. Direct applications of this result could be applied to motion-planning of a robot arm. We show that horizontal lifts to the pre-moduli space of paths in the moduli space can exhibit holonomy. We determine exactly which collections of side lengths allow holonomy.en
dc.description.degreePh. D.en
dc.identifier.otheretd-04152011-110946en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04152011-110946/en
dc.identifier.urihttp://hdl.handle.net/10919/26887en
dc.publisherVirginia Techen
dc.relation.haspartStClair_JL_D_2011.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectHolonomyen
dc.subjectRoboticsen
dc.subjectRiemannian Metricen
dc.subjectModuli Spaceen
dc.subjectPre-Moduli Spaceen
dc.subjectDifferential Geometryen
dc.titleGeometry of Spaces of Planar Quadrilateralsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
StClair_JL_D_2011.pdf
Size:
840.97 KB
Format:
Adobe Portable Document Format
Download

Collections

Doctoral Dissertations