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Statements

Subject Item
n2:RIV%2F00216224%3A14310%2F01%3A00004221%21RIV%2F2002%2FMSM%2F143102%2FN
rdf:type
skos:Concept n19:Vysledek
dcterms:description
Let $M$ be a differentiable manifold with a pseudo-Riemannian metric $g$ and a linear symmetric connection $K$. We classify all natural 0-order vector fields and 2-vector fields on $TM$ generated by $g$ and $K$. We get that all natural vector fields are linear combinations of the vertical lift of $u\in T_xM$ and the horizontal lift of $u$ with respect to $K$. Similarlz all natural 2-vector fields are linear combinatins of two canonical 2-vector fields induced by $g$ and $K$. Conditions for natural vector fields and natural 2-vector fields to define a Jacobi or a Poisson structure on $TM$ are disscused. Let $M$ be a differentiable manifold with a pseudo-Riemannian metric $g$ and a linear symmetric connection $K$. We classify all natural 0-order vector fields and 2-vector fields on $TM$ generated by $g$ and $K$. We get that all natural vector fields are linear combinations of the vertical lift of $u\in T_xM$ and the horizontal lift of $u$ with respect to $K$. Similarlz all natural 2-vector fields are linear combinatins of two canonical 2-vector fields induced by $g$ and $K$. Conditions for natural vector fields and natural 2-vector fields to define a Jacobi or a Poisson structure on $TM$ are disscused.
dcterms:title
Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold
skos:prefLabel
Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold
skos:notation
RIV/00216224:14310/01:00004221!RIV/2002/MSM/143102/N
n3:strany
143
n3:aktivita
n4:Z n4:P
n3:aktivity
P(GA201/99/0296), Z(MSM 143100009)
n3:cisloPeriodika
2
n3:dodaniDat
n8:2002
n3:domaciTvurceVysledku
n17:5886856
n3:druhVysledku
n14:J
n3:duvernostUdaju
n9:S
n3:entitaPredkladatele
n16:predkladatel
n3:idSjednocenehoVysledku
688278
n3:idVysledku
RIV/00216224:14310/01:00004221
n3:jazykVysledku
n15:eng
n3:klicovaSlova
Poisson structure, pseudo-Riemannian manifold, natural operator
n3:klicoveSlovo
n13:pseudo-Riemannian%20manifold n13:Poisson%20structure n13:natural%20operator
n3:kodStatuVydavatele
CZ - Česká republika
n3:kontrolniKodProRIV
[D97A4A16E94A]
n3:nazevZdroje
Archivum Mathematicum
n3:obor
n11:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:pocetUcastnikuAkce
0
n3:pocetZahranicnichUcastnikuAkce
0
n3:projekt
n18:GA201%2F99%2F0296
n3:rokUplatneniVysledku
n8:2001
n3:svazekPeriodika
37
n3:tvurceVysledku
Janyška, Josef
n3:zamer
n10:MSM%20143100009
s:issn
0044-8753
s:numberOfPages
18
n6:organizacniJednotka
14310