Affine connections for $2$-osculating vector fields and geodesics
Affine connections for $2$-osculating vector fields and geodesics
Starting with the work of \textit{A. M. Pastore} [ Rend. Accad. Naz. Sci. Detta XL, IV. Ser. 22-23, 135-148 (1972; Zbl 0414.53008); Rend. Mat. Appl., VII. Ser. 1, 177-190 (1981; Zbl 0477.53018)]\ the authors study the relationship between the geodesics with respect to a connection for 2-osculating vector fields and the curves which are projections of standard horizontal vector fields on certain reduced bundles of the bundle of 2-osculating frames on a manifold. Then they consider the corresponding affine principal bundles and characterize the geodesics of an affine connection as the curves whose developments are open intervals of straight lines.
- University of Salento Italy
- University of Bari Aldo Moro Italy
2-osculating vector fields, Linear and affine connections, affine connection, 2-osculating frames, 510
2-osculating vector fields, Linear and affine connections, affine connection, 2-osculating frames, 510
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