A note on F-planar mappings of manifolds with non-symmetric linear connection

Petrović, Miloš Z.; Stankovic, Mića S.

doi:10.1142/s0219887819500786

Cited by 7 publications

(6 citation statements)

References 17 publications

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“…By using the fact that the torsion tensor T 1 and the structure F are preserved under an equitorsion holomorphically projective mapping and by substituting (21) and (22) into (20) we obtain that…”

Section: Equitorsion Holomorphically Projective Mappingsmentioning

confidence: 99%

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Generalized para-Kähler spaces in Eisenhart’s sense admitting a holomorphically projective mapping

Petrović

2019

Filomat

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We relax the conditions related to the almost product structure and in such a way introduce a wider class of generalized para-Kähler spaces. Some properties of the curvature tensors as well as those of the corresponding Ricci tensors of these spaces are pointed out. We consider holomorphically projective mappings between generalized para-Kähler spaces in Eisenhart's sense. Also, we examine some invariant geometric objects with respect to equitorsion holomorphically projective mappings. These geometric objects reduce to the para-holomorphic projective curvature tensor in case of holomorphically projective mappings between usual para-Kähler spaces. dl(t) dt 0, t ∈ I, is said to be a holomorphically planar curve if for some functions ρ 1 and ρ 2 of a parameter t the following ordinary differential equation holds [27, 30] ∇ λ(t) λ(t) = ρ 1 (t)λ(t) + ρ 2 (t)Fλ(t),

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Section: Equitorsion Holomorphically Projective Mappingsmentioning

confidence: 99%

“…In the present paper we provide a more general definition of generalized para-Kähler spaces in Eisenhart's sense than the one given in [16]. These results as well as those concerning F-planar mappings given in [21] are included in the author's Ph.D. thesis [19].…”

Section: Introductionmentioning

confidence: 97%

Generalized para-Kähler spaces in Eisenhart’s sense admitting a holomorphically projective mapping

Petrović

2019

Filomat

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“…The F -planar mappings of symmetric affine connection spaces are involved by J. Mikeš and his research group [2][3][4][5][6][7]9,10]. This research is continued with F -planar mappings of non-symmetric affine connection spaces [11,16]. We are aimed to apply the formulas from [14] to obtain invariants for special F -planar mappings in this paper.…”

Section: Introductionmentioning

confidence: 99%

Invariants for F-Planar Mappings of Symmetric Affine Connection Spaces

Vesić

Mihajlović²

2022

FU Math Inform

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This research is motivated by similarity of basic equations of $F$-planar mappings of symmetric affine connection space $\mathbb A_N$ involved by J. Mike� and N. S. Sinyukov, and which have been studied by Mike��s research group (I. Hinterleitner, P. Pe\v ska, \linebreak J. Str\'ansk\'a) and almost geodesic mappings (specially almost geodesic mappings of the second type) ofthe space $\mathbb A_N$ involved by N. S. Sinyukov and which have been studied by many authors. We used the formulas obtained by N. O. Vesic to obtain invariants for special $F$-planar mappings in this article. These invariants are analogous to invariants of geodesic mappings (the Thomas projective parameter and the Weyl projective tensor).

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“…Afterwards, several types of a quarter-symmetric metric connection were studied ( [8,15,21,25,28]). In [11,20,22,26,31,32], the geometric and physic properties of conformal and projective the semi-symmetric metric recurrent connections were studied. And in [23,24] a projective conformal quarter-symmetric metric connection and a generalized quarter-symmetric metric recurrent connection were studied.…”

Section: Introductionmentioning

confidence: 99%