Conformal Mappings of Riemannian Spaces onto Ricci Symmetric Spaces

Berezovski, Volodymyr; Hinterleitner, Irena; Guseva, Nadezhda Ivanovna; Mikeš, Josef

doi:10.1134/s0001434618010315

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Introduction3

On Isopetrimetric Extremal Of Rotation and Rotary Mapping1

Contra Example Of Spaces Admitting Rotary Mappings1

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2019

2021

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Cited by 5 publications

(8 citation statements)

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“…The equations of the isoperimetric extremal of rotation were simplified by Mikeš, Stepanova and Sochor [24] to ∇ s λ = c · K · Fλ, where c is a constant, s is the arc length, F is a tensor 1 1 which satisfies the conditions…”

Section: On Isopetrimetric Extremal Of Rotation and Rotary Mappingmentioning

confidence: 99%

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Rotary mappings of spaces with affine connection

Mikeš

Rýparová

2019

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Section: On Isopetrimetric Extremal Of Rotation and Rotary Mappingmentioning

confidence: 99%

“…A necessary condition for a (pseudo-) Riemannian space V 2 to admit rotary mapping onto a manifoldĀ 2 is existence of a vector field that satisfies condition (1). Apparently, this vector field is a special type of torse-forming vector field which was defined by K. Yano [36], see also [19].…”

Section: Contra Example Of Spaces Admitting Rotary Mappingsmentioning

confidence: 99%

Rotary mappings of spaces with affine connection

Mikeš

Rýparová

2019

Filomat

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“…For geodesic mappings of generalized symmetric and recurrent spaces, such problems were solved by J. Mikeš, V.S. Sobchuk, and others [21][22][23][24][25][26][27][38][39][40][41][42][43][44][45][46][47][48]. There are many works devoted to issues of the theory of geodesic mappings, for example [49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Geodesic Mappings of Spaces with Affine Connections onto Generalized Symmetric and Ricci-Symmetric Spaces

et al. 2020

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In the paper, we consider geodesic mappings of spaces with an affine connections onto generalized symmetric and Ricci-symmetric spaces. In particular, we studied in detail geodesic mappings of spaces with an affine connections onto 2-, 3-, and m- (Ricci-) symmetric spaces. These spaces play an important role in the General Theory of Relativity. The main results we obtained were generalized to a case of geodesic mappings of spaces with an affine connection onto (Ricci-) symmetric spaces. The main equations of the mappings were obtained as closed mixed systems of PDEs of the Cauchy type in covariant form. For the systems, we have found the maximum number of essential parameters which the solutions depend on. Any m- (Ricci-) symmetric spaces (m≥1) are geodesically mapped onto many spaces with an affine connection. We can call these spaces projectivelly m- (Ricci-) symmetric spaces and for them there exist above-mentioned nontrivial solutions.

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“…De and Mandal in [3] studied concircular curvature tensors as important tensors from the differential geometric point of view. In [4][5][6][7][8][9][10][11], Mikeš et al have studied special kinds ot transformations in Riemannian space.…”

Section: Introductionmentioning

confidence: 99%