Conformal holomorphically projective mappings of almost Hermitian manifolds with a certain initial condition

In this paper, we study holomorphically projective and conformal holomorphically projective mappings between almost Hermitian manifolds H-n = (M, g, F) and (H) over bar(n) = ((M) over bar, (g) over bar, (F) over bar), i.e. diffeomorphism f : M -> (M) over bar satisfying f = f(1) omicron f(2) omicron f(3), where f(1), f(3) are conformal mappings and f(2) is a holomorphically projective mapping between almost Hermitian manifolds. We obtain fundamental equations of Cauchy type for holomorphically projective mappings between almost Hermitian manifolds and for above-mentioned mappings a new result for the initial condition f*(g) over bar = k center dot g.