On holomorphically projective mappings of generalized Kählerian spaces. (English) Zbl 1060.53014

The paper is a continuation of Minčić’s research of Riemannian spaces with nonsymmetric metric tensor \(g_{ij}\). Here only two of four kinds of covariant derivatives are used. The space is equipped with an almost complex structure \(F^i_j(x)\) and is denoted by \(GK_N\). A curve \(l:x^h=x^h(t)\) is an analytic planar curve if \(\lambda^h{}_{\underset\theta| p}\lambda^p=a(t)\lambda^h+b(t)F_p{}^h\lambda^p\), \(\theta=1,2\). A diffeomorphism \(f:GK_N\to G\overline K_N\) is holomorphically projective (h.p.) if the planar curves of the space \(GK_N\) are mapped into planar curves of the space \(G\overline K_N\). It is proved that \(HT_i{}^h{}_i\) is invariant under holomorphically projecture (h.p.) mappings. If the h.p. map is such that the torsion tensor satisfying \(\underset{\text v} {\overline\Gamma}_i{}^h{}_j= \underset{\text v}\Gamma_i{}^h{}_j\), then the h.p. map is called an equitorsion h.p. (e.h.p.) map. For e.h.p. maps two invariants are obtained connected with the curvature tensor of the first and second type.


53B05 Linear and affine connections
53A45 Differential geometric aspects in vector and tensor analysis
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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