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Jacobi fields, bundles and connections

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Authors
Väisänen, Olli
Date
2020
Discipline
MatematiikkaMathematics
Copyright
This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.

 
Tämä teksti käsittelee Jacobin kenttiä ja niiden määrittelemiseen tarvittavia rakenteita, erityisesti vektorikimppuja ja konnektioita. Lopputuloksena osoitetaan yksi yhteen-vastaavuus Jacobin kenttien ja geodeesiperheiden variaatiokenttien välillä.
 
This text discusses Jacobi fields and the structures needed in their definition, vector bundles and connections in particular. The one-to-one -correspondence between Jacobi fields and the variation fields of families of geodesics is proven as a final result.
 
Keywords
matematiikka differentiaaligeometria kuidut mathematics differential geometry fibres
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http://urn.fi/URN:NBN:fi:jyu-202009105811

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