On Holomorphically Projective Mappings Onto Riemannian Almost-Product Spaces

On holomorphically projective mappings of $e$-Kähler manifolds

“…Further we notice that for holomorphically projective mappings between e-Kähler manifolds K n andK n of class C 3 holds the following third set of equations [6,8,9,15,10,16]:…”

“…We present well known facts, which were proved by Domashev, Kurbatova, Mikeš, Prvanović, Otsuki, Tashiro etc., see [2,3,6,7,8,9,10,11,12,15,16,17,18,19]. In these results no details about the smoothness class of the metric were stressed.…”

On $F^\varepsilon _2$-planar mappings of (pseudo-) Riemannian manifolds

“…From that follows F 2 = κ Id, where κ is a function, which is in contradiction with our assumption. For this reason in the formula (22) we suppose that…”

Geodesic mappings of (pseudo-) Riemannian manifolds preserve class of differentiability

“…In 1978 (see [15] and PhD. thesis [14], and see [16,21,22], [23, p. 125], [25, p. 188]) Mikeš proved that under the conditions V n ,V n ∈ C 3 the following theorem holds (locally):…”

“…We briefly remind some main facts of geodesic mapping theory of (pseudo-) Riemannian manifolds which were found by T. Levi-Civita [13], L.P. Eisenhart [5,6] and N.S. Sinyukov [31], see [1,[9][10][11]14,16,18,19,23,[25][26][27][28][29][30][31][32][34][35][36]. In these results no details about the smoothness class of the metric were stressed.…”