Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F01%3A00004221" target="_blank" >RIV/00216224:14310/01:00004221 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold

Original language 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 arelinear combinations of the vertical lift of $uin T_xM$ 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F99%2F0296" target="_blank" >GA201/99/0296: Differential geometry of higher order</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2001

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Archivum Mathematicum

ISSN

0044-8753

e-ISSN

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Volume of the periodical

37

Issue of the periodical within the volume

2

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

18

Pages from-to

143

UT code for WoS article

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EID of the result in the Scopus database

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