KOLÁŘ, Ivan. Covariant Approach to Weil Bundles. 1st ed. Brno: Masarykova univerzita. 106 pp. ISBN 978-80-210-8385-1. 2016.
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Basic information
Original name Covariant Approach to Weil Bundles
Name in Czech Kovariantní přístup k Weilovým bandlům
Authors KOLÁŘ, Ivan.
Edition 1. vyd. Brno, 106 pp. 2016.
Publisher Masarykova univerzita
Other information
Original language English
Type of outcome Book on a specialized topic
Field of Study 10101 Pure mathematics
Country of publisher Czech Republic
Confidentiality degree is not subject to a state or trade secret
Publication form printed version "print"
ISBN 978-80-210-8385-1
Tags Munipress
Changed by Changed by: Mgr. Radka Vyskočilová, učo 2368. Changed: 18/5/2017 15:02.
Abstract
In the original definition by A. Weil, an infinitely near point on a smooth manifold M is introduced as a homomorphisms of the algebra of smooth functions C^\infty on M into a local (=Weil) algebra A. This point of view is close to algebraic geometry. On the other hand, there is the idea of (k; r)-velocity based on the concept of jet by C. Ehresmann, that seems to be more appropriate for differential geometry. The author introduces an original concept of A-velocity, that unifies both points of view. Beside the geometry of Weil bundles, some further jet-like functors are studied. The last Chapter 8 is devoted to nonholonomic jets, non-holonomic contact elemets and their applications to the submanifolds of Cartan spaces.
Abstract (in Czech)
Kniha se zabývá původním konceptem A. Weila, který odpovídá algebraické geometrii, a alternativnim konceptem C. Ehresmanna, který má blíže k diferenciální geometrii. Následně představuje svůj vlastní koncept A-rychlosti, který oba náhledy sjednocuje.
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