Canonical almost geodesic mappings of type $\underset\theta\pi{}_2(0,F)$, ${\small\theta\in\{1,2\}}$ between generalized parabolic K\"ahler manifolds

Petrović, Miloš Z.

doi:10.18514/mmn.2018.1908

Cited by 12 publications

(9 citation statements)

References 8 publications

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“…On the other hand we gave a more general definition of generalized Kähler spaces in Eisenhart's sense [22]. In the same manner generalized m-parabolic Kähler spaces were defined in [17,18]. A new type of generalized para-Kähler space is given in [23].…”

Section: Introductionmentioning

confidence: 99%

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

Petrović

2019

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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: Introductionmentioning

confidence: 99%

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

Petrović

2019

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“…Minčć [10-14, 21, 26]. Further, generalized elliptic, hyperbolic and parabolic Kählerian spaces were developed in [14,[17][18][19][20]26]. Recently, generalized m-parabolic Kähler manifolds were defined in [18].…”

Section: Introductionmentioning

confidence: 99%

Equitorsion holomorphically projective mappings of generalized m-parabolic Kähler manifolds

Petrović

Peška²

2019

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We investigate equitorsion holomorphically projective mappings of generalized m-parabolic Kähler manifolds and provide some necessary and sufficient conditions for the existence of these mappings in form of linear PDE-systems. Also, we find an invariant geometric object with respect to a holomorphically projective mapping of generalized m-parabolic Kähler manifolds which is analogous to the Thomas projective parameter. Definition 1.1. [18]A generalized Riemannian manifold (M, ) of even dimension n (n > 2) is said to be a generalized m-parabolic Kähler manifold if there exists a tensor field F on M of type (1, 1) such that rank(F) = m ≤ n 2 and the following conditions hold

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“…Some physical characteristics of conformal mappings were given in [5]. Geodesic mappings and their generalizations is an active research field, see for instance [6][7][8][9][10][11][12][13][14][15]. Some conformal and projective invariants of Riemannnian manifolds were obtained by Reference [16,17].…”

Section: Introductionmentioning

confidence: 99%

On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces

2019

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We consider conformal and concircular mappings of Eisenhart's generalized Riemannian spaces. We prove conformal and concircular invariance of some tensors in Eisenhart's generalized Riemannian spaces. We give new generalizations of symmetric spaces via Eisenhart's generalized Riemannian spaces. Finally, we describe some properties of covariant derivatives of tensors analogous to Yano's tensor of concircular curvature in Eisenhart symmetric spaces of various kinds.

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Canonical almost geodesic mappings of type $\underset\theta\pi{}_2(0,F)$, ${\small\theta\in\{1,2\}}$ between generalized parabolic K\"ahler manifolds

Cited by 12 publications

References 8 publications

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

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

Equitorsion holomorphically projective mappings of generalized m-parabolic Kähler manifolds

On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces

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