![]() ; Grong, Erlend ![]() E-print/Working paper (2015) 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 ... [more ▼] 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). [less ▲] Detailed reference viewed: 124 (3 UL) |
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