Abstract
The notions of ordinary, covariant and Lie differentials are considered as operators over differentiable manifolds with different (not only by sign) contravariant and covariant affine connections and metric. The difference between the interpretations of the ordinary differential as a covariant basic vector field and as a component of a contravariant vector field is discussed. By means of the covariant metric and the ordinary differential the notion of the line element is introduced and the geodesic equation is obtained and compared with the autoparallel equation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.