Almost Geodesics and Special Affine Connection

Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces

“…Sobchuk [19,20], N.Y. Yablonskaya [21,22], V.E. Berezovski, J. Mikeš [14,15,[23][24][25][26][27][28][29][30][31][32][33][34][35], O. Belova, J. Mikeš, K. Strambach [36,37], M.S. Stankovič, Lj.S.…”

“…) could be written in such form as(n + 1)a iρ 1 ,jρ 2 ...ρ m − a jρ 1 ,iρ 2 ...ρ m − a ij,ρ 1 ρ 2 ...ρ m = −Ω ijρ 1 ρ 2 ...ρ m . (36)Let us interchange the indices j and ρ 1 in(36) and symmetrize in the indices i and ρ 1 . Then we have a ij,ρ 1 ρ 2 ...ρ m + a jρ 1 ,iρ 2 ...ρ m = − 1 n Ω (iρ 1 )jρ 2 ...ρ m + 2 n a iρ 1 , jρ 2 ...ρ m .…”

Generalized Affine Connections Associated with the Space of Centered Planes

“…The theory of affine connections is widely used in physics [17][18][19][20][21] and by studying geodesics [22] (see, e.g., [23][24][25][26][27][28]).…”