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

Stanković, Mića S.; Minčić, Svetislav M.; Velimirović, Ljubica S.

Mat. Vesn. 54, No. 3-4, 195-202 (2002).

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.

Reviewer: Irena Čomić (Novi Sad)

MSC:

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.)