Almost geodesics and special affine connection

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73602014" target="_blank" >RIV/61989592:15310/20:73602014 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs00025-020-01251-y" target="_blank" >https://link.springer.com/article/10.1007%2Fs00025-020-01251-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-020-01251-y" target="_blank" >10.1007/s00025-020-01251-y</a>

Result language
angličtina
Original language name
Almost geodesics and special affine connection
Original language description
In the present paper we continue to study almost geodesic curves and determine in Rn the form of curves C for which every image under an (n- 1 ) -dimensional algebraic torus is also an almost geodesic with respect to an affine connection ∇ with constant coefficients. We also calculate explicitly the components of ∇. For the explicit calculation of the form of curves C in the n-dimensional real space Rn that are almost geodesics with respect to an affine connection ∇ , we can suppose that with C all images of C under a real (n- 1 ) -dimensional algebraic torus are also almost geodesics. This implies that the determination of C becomes an algebraic problem. Here we use E. Beltrami’s result that a differentiable curve is a local geodesic with respect to an affine connection ∇ precisely if it is a solution of an abelian differential equation with coefficients that are functions of the components of ∇. Now we consider the special case for the connection ∇ in which every curve is almost geodesic with respect to ∇.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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