Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind

Abstract

Starting from the definition of generalized Riemannian space (GR N ) [5], in which a non-symmetric basic tensor g ij is introduced, in the present paper a generalized Kählerian space GK 2 N of the second kind is defined, as a GR N with almost complex structure F h i , that is covariantly constant with respect to the second kind of covariant derivative (equation (2.3)).We observe hollomorphically projective mapping of the spaces GK 2 N and GK 2 N with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces, and for them we find invariant geometric objects.

Invariants of Special Second-Type Almost Geodesic Mappings of Generalized Riemannian Space

“…Different mappings of Riemannian and generalized Riemannian spaces as well as their invariants have been investigated (see [1,2,6,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]28,29,31]). N. S. Sinyukov started the research about almost geodesic mappings [19].…”

Geodesic mapping onto Kählerian spaces of the first kind

“…Kählerian spaces and their mappings were investigated by many authors, for example T. Otsuki and Y. Tasiro [18], [25], K. Yano [26], J. Mikeš, V. V. Domashev [1], [6], [7], [8], [9], [10], [11], [22], M. Prvanović [19], N. Pušić [21], S. S. Pujar [20], M. S. Stanković at al. [16], [24], and many others.…”

On canonical F-planar mappings of spaces with affine connection

“…The quasi geodesic mappings was defined by A.Z. Petrov and they are very close to holomorphically projective mappings of Kähler spaces studied by T. Otsuki, Y. Tashiro, M. Prvanović, J. Mikeš etc., see [18,19,22,26,30,33,38].…”