Geodesic Mapping onto Riemannian Manifolds and Differentiability

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F17%3A73583842" target="_blank" >RIV/61989592:15310/17:73583842 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.7546/giq-18-2017-183-190" target="_blank" >http://dx.doi.org/10.7546/giq-18-2017-183-190</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7546/giq-18-2017-183-190" target="_blank" >10.7546/giq-18-2017-183-190</a>

Result language
angličtina
Original language name
Geodesic Mapping onto Riemannian Manifolds and Differentiability
Original language description
In this paper we study fundamental equations of geodesic mappings of manifolds with affine connection onto (pseudo-) Riemannian manifolds. We proved that if a manifold with affine (or projective) connection of differentiability class Cr (r >1) admits a geodesic mapping onto a (pseudo-) Riemannian manifold of class C1, then this manifold belongs to the differentiability class C(r+1). From this result follows if an Einstein spaces admits non-trivial geodesic mappings onto (pseudo-) Riemannian manifolds of class C1 then this manifold is an Einstein space, and there exists a common coordinate system in which the components of the metric of these Einstein manifolds are real analytic functions.
Czech name
—
Czech description
—

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)