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  • In this paper we present the theory of higher order velocities and their scalar differential invariants. We consider a natural action of a differential group on manifolds of higher order velocities and study properties of its orbits (contact elements) and orbit spaces (higher order Grassmann bundles). We show that this action defines on a manifold of regular velocities the structure of a principal fibre bundle with structure group the differential group. The bundle projection is then naturally interpreted as the basis of scalar invariants of higher order velocities. We give a recurrence formula for differential invariants. Explicit description of the basis is given for velocities of order less or equal 3. Analogous methods can be applied to the problem of finding bases of differential invariants of different geometric objects.
  • In this paper we present the theory of higher order velocities and their scalar differential invariants. We consider a natural action of a differential group on manifolds of higher order velocities and study properties of its orbits (contact elements) and orbit spaces (higher order Grassmann bundles). We show that this action defines on a manifold of regular velocities the structure of a principal fibre bundle with structure group the differential group. The bundle projection is then naturally interpreted as the basis of scalar invariants of higher order velocities. We give a recurrence formula for differential invariants. Explicit description of the basis is given for velocities of order less or equal 3. Analogous methods can be applied to the problem of finding bases of differential invariants of different geometric objects. (en)
  • V článku se zabýváme teorií rychlostí vyššího řádu a jejich skalárními invarianty. Uvažujeme přirozenou akci diferenciální grupy na varietě rychlostí vyššího řádu a studujeme její orbity (kontaktní elementy) a prostory orbit (Grassmannovy fibrace). Ukazujeme, že tato akce definuje na varietě rychlostí strukturu hlavního fibrovaného prostoru, jehož strukurní grupa je diferenciální grupa. Projekce tohoto fibrovaného prostoru je pak báze skalárních invariantů. Odvozujeme rekurenční vzorec pro diferenciální invarianty a nalézáme explicitní charakteristiky bází invariantů řádu menšího nebo rovného třem. Obdobné metody mohou být uplatněny pro vyšetřování diferenciálních invariantů jiných geomerických objektů. (cs)
Title
  • Differential invariants and higher order Grassmann bundles
  • Differential invariants and higher order Grassmann bundles (en)
  • Diferenciální invarianty a Grassmannova rozvrstvení vyššího řádu (cs)
skos:prefLabel
  • Differential invariants and higher order Grassmann bundles
  • Differential invariants and higher order Grassmann bundles (en)
  • Diferenciální invarianty a Grassmannova rozvrstvení vyššího řádu (cs)
skos:notation
  • RIV/61989592:15310/08:00005362!RIV09-MSM-15310___
http://linked.open...avai/riv/aktivita
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  • P(GA201/06/0922), Z(MSM6198959214)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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  • 363567
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  • RIV/61989592:15310/08:00005362
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  • Differential invariant; Grassmann bundle (en)
http://linked.open.../riv/klicoveSlovo
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  • [494CC7EF2C0F]
http://linked.open...i/riv/mistoVydani
  • Singapore
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  • Differential Geometry and its Applications, Proceedings of 10th International Conference on Differential Geometry & Applications
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  • Krupka, Demeter
  • Urban, Zbyněk
http://linked.open...n/vavai/riv/zamer
number of pages
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  • World Scientific
https://schema.org/isbn
  • 978-981-279-060-6
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  • 15310
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