F-geodesics on Manifolds

作者：Bejan Cornelia Livia^*; Druta Romaniuc Simona Luiza

来源：Filomat, 2015, 29(10): 2367-2379.

DOI：10.2298/FIL1510367B

• geodesic
• magnetic curve
• projective transformation
• holomorphically projective transformation
• C-projective transformation
• foliated manifold
• almost contact manifold
• Vranceanu connection

The notion of F geodesic, which is slightly different from that of F planar curve (see [13], [17], and [18]), generalizes the magnetic curves, and implicitly the geodesics, by using any (1,1)-tensor field on the manifold (in particular the electro-magnetic field or the Lorentz force). We give several examples of F-geodesics and the characterizations of the F-geodesics w.r.t. Vranceanu connections on foliated manifolds and adapted connections on almost contact manifolds. We generalize the classical projective transformation, holomorphic-projective transformation and C-projective transformation, by considering a pair of symmetric connections which have the same F-geodesics. We deal with the transformations between such two connections, namely F-planar diffeomorphisms ([18]). We obtain a Weyl type tensor field, invariant under any F-planar diffeomorphism, on a 1-codimensional foliation.

• 出版日期2015