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Description
  • Je formulován problém nalezení všech diferenciálních invariantů r-tého řádu z vnoření variet s metrickými poli, s hodnotami v levé (G^1_m x G^1_n)-varietě. Báze invariantů je získána pomocé metody redukce orbit. Jako nový výsledek je dokázáno, že diferenciální invarianty r-tého řádu z vnoření f:M->N variet M a N s metrickými poli lze faktorizovet vzhledem k metrikám, křivostem a jejich kovarintním rerivacím do řádu (r-2) a kovariantnímu diferenciálu tečného zobrazení Tf do řádu r. poslední pojem je v práci nově zaveden. Získané výsledky jsou interpretovány geometricky. (cs)
  • The problem of finding all r-th order differential invariants of immersions of manifolds with metric fields, with values in a left (G^1_m x G^1_n)-manifold is formulated. For obtaining the basis of higher order differential invariants the orbit reduction method is used. As a new result it appears that r-th order differential invariants depending on an immersion f:M->N of manifolds M and N and on metric fields on them can be factorized through metrics, curvature tensors and their covariant derivatives up to the order (r-2), and covariant differentials of the tangent mapping Tf up to the order r. The concept of a covariant differential Tf is also introduced in this paper. The obtained results are geometrically interpreted as well.
  • The problem of finding all r-th order differential invariants of immersions of manifolds with metric fields, with values in a left (G^1_m x G^1_n)-manifold is formulated. For obtaining the basis of higher order differential invariants the orbit reduction method is used. As a new result it appears that r-th order differential invariants depending on an immersion f:M->N of manifolds M and N and on metric fields on them can be factorized through metrics, curvature tensors and their covariant derivatives up to the order (r-2), and covariant differentials of the tangent mapping Tf up to the order r. The concept of a covariant differential Tf is also introduced in this paper. The obtained results are geometrically interpreted as well. (en)
Title
  • Differential Invariants of Immersions of Manifolds with Metric Fields
  • Differential Invariants of Immersions of Manifolds with Metric Fields (en)
  • Diferenciální invarianty z vnoření variet s metrickými poli (cs)
skos:prefLabel
  • Differential Invariants of Immersions of Manifolds with Metric Fields
  • Differential Invariants of Immersions of Manifolds with Metric Fields (en)
  • Diferenciální invarianty z vnoření variet s metrickými poli (cs)
skos:notation
  • RIV/00216224:14310/04:00010215!RIV09-GA0-14310___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/03/0512), Z(MSM 143100006)
http://linked.open...iv/cisloPeriodika
  • 2
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 560574
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14310/04:00010215
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • smooth manifolds; differential invariants (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [6DC65568A0EA]
http://linked.open...i/riv/nazevZdroje
  • Communications in Mathematical Physics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 249
http://linked.open...iv/tvurceVysledku
  • Musilová, Jana
  • Musilová, Pavla
http://linked.open...ain/vavai/riv/wos
  • 000222914800005
http://linked.open...n/vavai/riv/zamer
issn
  • 0010-3616
number of pages
http://localhost/t...ganizacniJednotka
  • 14310
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