Special \(F\)-planar mappings of affinely connected spaces onto Riemannian spaces (Q1358367)

The paper deals with \(F_1\)-planar mappings of affinely connected spaces \(A_n\) onto Riemannian spaces \(V_n(g_{ij})\) that are \(F\)-planar mappings for which the conditions \(g_{si}F^s_j+ g_{sj}F^s_i= 0\) are satisfied for the structural affinor \(F\). These mappings generalize the quasigeodesic and holomorphically projective mappings introduced by A. Z. Petrov, T. Otsuki, I. Tashiro and M. Prvanović. The main equations of \(F_1\)-planar mappings have been shown to be representable as a closed system of differential equations in Cauchy-type covariant derivatives on \((n+1)(n+2)/2\) unknown functions. Particular cases are illustrated, in which the main equations are represented as a linear system.