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• W2220787599 abstract "We introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle $D$ of the tangent bundle. We provide explicit means of computing these holonomy groups by deriving analogues of Ambrose-Singer's and Ozeki's theorems. We then give necessary and sufficient conditions in terms of the horizontal holonomy groups for existence of solutions of two problems on foliated manifolds: determining when a foliation can be either (a) totally geodesic or (b) endowed with a principal bundle structure. The subbundle $D$ plays the role of an orthogonal complement to the leaves of the foliation in case (a) and of a principal connection in case (b)." @default.
• W2220787599 created "2016-06-24" @default.
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• W2220787599 date "2015-11-18" @default.
• W2220787599 modified "2023-10-15" @default.
• W2220787599 title "Horizontal holonomy and foliated manifolds" @default.
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• W2220787599 doi "https://doi.org/10.48550/arxiv.1511.05830" @default.
• W2220787599 hasPublicationYear "2015" @default.
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