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On Geodesics of Sprays and Projective Completeness | | Guojun Yang
; | | Date: |
2 Jan 2023 | | Abstract: | Geodesics, which play an important role in spray-Finsler geometry, are
integral curves of a spray vector field on a manifold. Some comparison theorems
and rigidity issues are established on the completeness of geodesics of a spray
or a Finsler metric. In this paper, projectively flat sprays with weak Ricci
constant (eps. constant curvature) are classified at the level of geodesics.
Further, a geodesic method is introduced to determine an $n$-dimensional spray
based on a family of curves with $2(n-1)$ free constant parameters as
geodesics. Finally, it shows that a spray is projectively complete under
certain condition satisfied by the domain of geodesic parameter of all
geodesics. | | Source: | arXiv, 2301.00507 | | Services: | Forum | Review | PDF | Favorites | |
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