A generalized second-order frame bundle for Fréchet manifolds |
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| Institution: | 1. School of Mathematics, Manchester University, Manchester M60 1QD, UK;2. Section of Mathematics, Naval Academy of Greece, Xatzikyriakion, Piraeus 18539, Greece;3. Department of Mathematics, University of Athens, Panepistimiopolis, Athens 15784, Greece;1. Iris Adlershof, Humboldt-Universität zu Berlin, Zum Grossen Windkanal 2, Berlin, 12489, Germany;2. AIMS South Africa, 6 Melrose Road, Muizenberg, Cape Town, 7945, South Africa;3. Imperial College London, Prince Consort Rd, Kensington, London, SW7 2BW, United Kingdom of Great Britain and Northern Ireland;1. Philipps–Universität Marburg, Fachbereich für Mathematik und Informatik, Hans-Meerwein-Straße, 35032 Marburg, Germany;2. Università di Chieti-Pescara, Dipartimento di Economia, viale della Pineta 4, I-65129 Pescara, Italy;1. Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/ Nicolás Cabrera 15, Campus Cotoblanco UAM, E-28049 Madrid, Spain;2. Departamento de Matemática Aplicada II (ETSI Telecomunicación), Universidade de Vigo, Lagoas-Marcosende, 36310, Vigo (Pontevedra), Spain |
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| Abstract: | Working within the framework of Fréchet modelled infinite-dimensional manifolds, we propose a generalized notion of second-order frame bundle. We revise in this way the classical notion of bundles of linear frames of order 2, the direct definition and study of which is problematic due to intrinsic difficulties of the space models. However, this new structure keeps all the fundamental characteristics of a frame bundle. It is a principal Fréchet bundle associated (differentially and geometrically) with the corresponding second-order tangent bundle. |
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