{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:soar.wichita.edu:10057/10941"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:soar.wichita.edu:10057/10941","repository":{"repo_id":"wichita-thes","name":"Wichita State University","base_url":"https://soar.wichita.edu/oai/request"},"display":{"title":"Geometry of horizontal bundles and connections","abstract":"An Ehresmann connection on a fiber bundle pi: E --> M is defined by prescribing a suitable horizontal subbundle H of the tangent bundle piT: TE --> E. For a horizontal bundle to be suitable, it must have a property called horizontal path lifting. This property ensures that the horizontal bundle determines a system of parallel transport between the fibers of E. The main result of this dissertation is a geometric characterization of the horizontal bundles on E that have horizontal path lifting, and hence are connections. In particular, it is shown that a horizontal bundle has horizontal path lifting if and only if its horizontal spaces are bounded away from the vertical spaces, uniformly along fibers of E. In order for a horizontal bundle to admit a system of parallel transport or have holonomy, it must be a connection. However, certain other geometric properties that are usually attributed to connections are actually properties of arbitrary horizontal bundles. These properties are studied in the case when E is either a vector bundle or tangent bundle, accordingly.","abstract_html":"An Ehresmann connection on a fiber bundle pi: E --> M is defined by prescribing a suitable horizontal subbundle H of the tangent bundle piT: TE --> E. For a horizontal bundle to be suitable, it must have a property called horizontal path lifting. This property ensures that the horizontal bundle determines a system of parallel transport between the fibers of E. The main result of this dissertation is a geometric characterization of the horizontal bundles on E that have horizontal path lifting, and hence are connections. In particular, it is shown that a horizontal bundle has horizontal path lifting if and only if its horizontal spaces are bounded away from the vertical spaces, uniformly along fibers of E. In order for a horizontal bundle to admit a system of parallel transport or have holonomy, it must be a connection. However, certain other geometric properties that are usually attributed to connections are actually properties of arbitrary horizontal bundles. These properties are studied in the case when E is either a vector bundle or tangent bundle, accordingly.","abstract_has_math":false,"creators":["Ryan, Justin M."],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-05","date_published":"2014-05","updated_at":"2026-07-24T06:05:48Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/10941"],"render_values":[{"text":"hdl:10057/10941","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2014-05"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/10941"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["An Ehresmann connection on a fiber bundle pi: E --> M is defined by prescribing a suitable horizontal subbundle H of the tangent bundle piT: TE --> E. For a horizontal bundle to be suitable, it must have a property called horizontal path lifting. This property ensures that the horizontal bundle determines a system of parallel transport between the fibers of E. The main result of this dissertation is a geometric characterization of the horizontal bundles on E that have horizontal path lifting, and hence are connections. In particular, it is shown that a horizontal bundle has horizontal path lifting if and only if its horizontal spaces are bounded away from the vertical spaces, uniformly along fibers of E. In order for a horizontal bundle to admit a system of parallel transport or have holonomy, it must be a connection. However, certain other geometric properties that are usually attributed to connections are actually properties of arbitrary horizontal bundles. These properties are studied in the case when E is either a vector bundle or tangent bundle, accordingly."]},{"key":"dc:title","label":"Title","values":["Geometry of horizontal bundles and connections"]}]}],"canonical_facts":{"dc:date.issued":["2014-05"],"dc:description.other":["An Ehresmann connection on a fiber bundle pi: E --> M is defined by prescribing a suitable horizontal subbundle H of the tangent bundle piT: TE --> E. For a horizontal bundle to be suitable, it must have a property called horizontal path lifting. This property ensures that the horizontal bundle determines a system of parallel transport between the fibers of E. The main result of this dissertation is a geometric characterization of the horizontal bundles on E that have horizontal path lifting, and hence are connections. In particular, it is shown that a horizontal bundle has horizontal path lifting if and only if its horizontal spaces are bounded away from the vertical spaces, uniformly along fibers of E. In order for a horizontal bundle to admit a system of parallel transport or have holonomy, it must be a connection. However, certain other geometric properties that are usually attributed to connections are actually properties of arbitrary horizontal bundles. These properties are studied in the case when E is either a vector bundle or tangent bundle, accordingly."],"dc:identifier":["hdl:10057/10941"],"dc:title":["Geometry of horizontal bundles and connections"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T06:05:48Z"}