On $F^\varepsilon _2$-planar mappings of (pseudo-) Riemannian manifolds

Hinterleitner, Irena; Mikeš, Josef; Peška, Patrik

doi:10.5817/am2014-5-287

Cited by 8 publications

(8 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now, we will provide the basic definitions and properties of F-planar mappings, which is possible to find in monograph [19, p. 385], and in the paper [12].…”

Section: Basic Concepts Of the Theory Of F-planar Mappings Of Space Wmentioning

confidence: 99%

“…for any tangent vectors X, Y, where ψ, ϕ are linear forms. Moreover, this mapping preserves affinor structuresF = α • F + β • I, see [12,25], [19, p. 385-392].…”

Section: Definition 22 (Mikeš Sinyukov [25] See [22 P 213])mentioning

confidence: 99%

“…The basic equations of F-planar mappings, which were obtained in the work by J. Mikeš and N.S. Sinyukov [25], have recently been clarified in [12]. The next study of F-planar mappings is possible to find in [14] and also in [2,19].…”

Section: Introductionmentioning

confidence: 99%

“…The next study of F-planar mappings is possible to find in [14] and also in [2,19]. In the paper [12], there was proved that PQ ε -equivalence, defined by P. Topalov, are previously studied F 2 -planar mappings. For this reason, we introduced the concept of F 2 ε -planar mappings.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On canonical F-planar mappings of spaces with affine connection

Berezovski

Mikeš

Peška

et al. 2019

Filomat

View full text Add to dashboard Cite

In this paper we study the theory of F-planar mappings of spaces with affine connection. We obtained condition, which preserved the curvature tensor. We also studied canonical F-planar mappings of space with affine connection onto symmetric spaces. In this case, the main equations have the partial differential Cauchy type form in covariant derivatives. We got the set of substantial real parameters on which depends the general solution of that PDE's system.

show abstract

“…Now, we will provide the basic definitions and properties of F-planar mappings, which is possible to find in monograph [19, p. 385], and in the paper [12].…”

Section: Basic Concepts Of the Theory Of F-planar Mappings Of Space Wmentioning

confidence: 99%

“…for any tangent vectors X, Y, where ψ, ϕ are linear forms. Moreover, this mapping preserves affinor structuresF = α • F + β • I, see [12,25], [19, p. 385-392].…”

Section: Definition 22 (Mikeš Sinyukov [25] See [22 P 213])mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On canonical F-planar mappings of spaces with affine connection

Berezovski

Mikeš

Peška

et al. 2019

Filomat

View full text Add to dashboard Cite

show abstract

“…The PQ ε -projective equivalence between n-dimensional Riemannian manifolds were introduced by Topalov [32], P and Q are tensors of type (1,1) for which PQ = ε Id, ε ∈ R, ε 1, 1 + n. Moreover, these mappings are special cases of F 2 -planar mappings, [8], studied in [19], see [24, p. 225 -231].…”

Section: Introductionmentioning

confidence: 99%

On Fε2-planar mappings with function ε of (pseudo-)Riemannian manifolds

Chudá

Guseva

Peška

2017

Filomat

View full text Add to dashboard Cite

In this paper we study special mappings between n-dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced PQ?-projectivity of Riemannian metrics, with constant ? ? 0,1 + n. These mappings were studied later by Matveev and Rosemann and they found that for ? = 0 they are projective. These mappings could be generalized for case, when ? will be a function on manifold. We show that PQ?- projective equivalence with ? is a function corresponds to a special case of F-planar mapping, studied by Mikes and Sinyukov (1983) with F = Q. Moreover, the tensor P is derived from the tensor Q and non-zero function ?. We assume that studied mappings will be also F2-planar (Mikes 1994). This is the reason, why we suggest to rename PQ? mapping as F?2. For these mappings we find the fundamental partial differential equations in closed linear Cauchy type form and we obtain new results for initial conditions.

show abstract