Closed Affine Manifolds with an Invariant Line

dc.contributor.advisorGoldman, William Men_US
dc.contributor.authorDaly, Charles Yvesen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2021-09-22T05:31:24Z
dc.date.available2021-09-22T05:31:24Z
dc.date.issued2021en_US
dc.description.abstractRadiant manifolds are affine manifolds whose holonomy preserves a point. Here we discuss certain properties of closed affine manifolds whose holonomy preserves an affine line. Particular attention is given to the case wherein the holonomy acts on the invariant line by translations and reflections. We show that in this case, the developing image must avoid the translation invariant line providing a generalization to the well known fact that closed radiant affine manifolds cannot have their fixed points inside the developing image. We conclude by generalizing this result to translation and reflection invariant proper subspaces of the holonomy.en_US
dc.identifierhttps://doi.org/10.13016/rrho-kqry
dc.identifier.urihttp://hdl.handle.net/1903/27911
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledAffineen_US
dc.subject.pquncontrolledDevelopingen_US
dc.subject.pquncontrolledHolonomyen_US
dc.subject.pquncontrolledInvarianten_US
dc.subject.pquncontrolledManifolden_US
dc.subject.pquncontrolledMapen_US
dc.titleClosed Affine Manifolds with an Invariant Lineen_US
dc.typeDissertationen_US

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