On Fε 2-planar mappings with function ε of (Pseudo-) Riemannian manifolds

Chudá, Hana; Guseva, Nadezda; Peška, Patrik

dc.title	On Fε 2-planar mappings with function ε of (Pseudo-) Riemannian manifolds	en
dc.contributor.author	Chudá, Hana
dc.contributor.author	Guseva, Nadezda
dc.contributor.author	Peška, Patrik
dc.relation.ispartof	Filomat
dc.identifier.issn	0354-5180 Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued	2017
utb.relation.volume	31
utb.relation.issue	9
dc.citation.spage	2683
dc.citation.epage	2689
dc.type	article
dc.language.iso	en
dc.publisher	University of Nis
dc.identifier.doi	10.2298/FIL1709683C
dc.relation.uri	http://www.doiserbia.nb.rs/img/doi/0354-5180/2017/0354-51801709683C.pdf
dc.subject	(pseudo-) Riemannian manifolds	en
dc.subject	F-planar mapping	en
dc.subject	Fε 2 -planar mapping	en
dc.subject	PQε -projective mapping	en
dc.description.abstract	In this paper we study special mappings between n-dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced PQε - projectivity of Riemannian metrics, with constant ε ≠ 0, 1 + n. These mappings were studied later by Matveev and Rosemann and they found that for ε = 0 they are projective. These mappings could be generalized for case, when ε will be a function on manifold. We show that PQε - projective equivalence with ε 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 ε. We assume that studied mappings will be also F2 - planar (Mikeš 1994). This is the reason, why we suggest to rename PQε mapping as Fε 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. © 2017, University of Nis. All rights reserved.	en
utb.faculty	Faculty of Applied Informatics
dc.identifier.uri	http://hdl.handle.net/10563/1007367
utb.identifier.obdid	43877717
utb.identifier.scopus	2-s2.0-85017632017
utb.identifier.wok	000408376500012
utb.source	j-scopus
dc.date.accessioned	2017-09-08T12:14:46Z
dc.date.available	2017-09-08T12:14:46Z
dc.description.sponsorship	Fac. of Appl. Informatics, T. Bata University in Zlin [CZ.1.07/2.3.00/30.0035]; Palacky University Olomouc [IGA PrF 2014016]
utb.contributor.internalauthor	Chudá, Hana
utb.fulltext.affiliation	Hana Chudá a, Nadezda Guseva b, Patrik Peška c a Tomas Bata University of Zlin, Faculty of Applied Informatics, Dept. of Math. b Moscow Pedagogical University, Dept. of Geometry c Palacky University Olomouc, Dept. of Algebra and Geometry Email addresses: chuda@fai.utb.cz (Hana Chudá), ngus12@mail.ru (Nadezda Guseva), patrik.peska@upol.cz (Patrik Peška)
utb.fulltext.dates	-
utb.fulltext.references	[1] H. Chudá, M. Shiha, Conformal holomorphically projective mappings satisfying a certain initial condition, Miskolc Math. Notes 14 (2013) 569–574. [2] I. Hinterleitner, On holomorphically projective mappings of e-Kähler manifolds, Arch. Mat. (Brno) 48 (2012) 333–338. [3] I. Hinterleitner, J. Mikeš, On F-planar mappings of spaces with affine connections, Note Mat. 27 (2007) 111–118. [4] I. Hinterleitner, J. Mikeš, Fundamental equations of geodesic mappings and their generalizations, J. Math. Sci. 174 (2011) 537–554. [5] I. Hinterleitner, J. Mikeš, Projective equivalence and spaces with equi-affine connection, J. Math. Sci. 177 (2011) 546–550; transl. from Fundam. Prikl. Mat. 16 (2010) 47–54. [6] I. Hinterleitner, J. Mikeš, Geodesic Mappings and Einstein Spaces, in Geom. Meth. in Phys., Birkhäuser, Basel 19 (2013) 331–336. [7] I. Hinterleitner, J. Mikeš, On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds, Arch. Math. 49 (2013) 295–302 [8] I. Hinterleitner, J. Mikeš, P. Peška, On F ε 2 - planar mappings of (pseudo-) Riemannian manifolds, Arch. Math. 50 (2014) 287–295. [9] I. Hinterleitner, J. Mikeš, J. Stránská, Infinitesimal F-planar transformations, Russ. Math. 52 (2008) 13–18. [10] J. Hrdina, Almost complex projective structures and their morphisms, Arch. Math. 45 (2009) 255–264. [11] J. Hrdina, J. Slovák, Morphisms of almost product projective geometries, Proc. 10th Int. Conf. on Diff. Geom. and its Appl., DGA 2007, Olomouc. Hackensack, NJ: World Sci. (2008) 253–261. [12] J. Hrdina, P. Vašík, Generalized geodesics on almost Cliffordian geometries, Balkan J. Geom. Appl. 17 (2012) 41–48 [13] M. Jukl, L. Juklová, J. Mikeš, Some results on traceless decomposition of tensors, J. Math. Sci. 174 (2011) 627–640. [14] R.J.K. al Lami, M. Škodová, J. Mikeš, On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces, Arch. Math. 42 (2006) 291–299. [15] T. Levi-Civita, Sulle transformationi delle equazioni dinamiche, Ann. Mat. Milano 24 (1886) 255–300. [16] V. Matveev, S. Rosemann, Two remarks on PQ ε -projectivity of Riemanninan metrics, Glasgow Math. J. 55 (2013) 131–138. [17] J. Mikeš, On holomorphically projective mappings of Kählerian spaces, Ukr. Geom. Sb. 23 (1980) 90–98. [18] J. Mikeš, Special F-planar mappings of affinely connected spaces onto Riemannian spaces, Mosc. Univ. Math. Bull. 49 (1994) 15–21. [19] J. Mikeš, Holomorphically projective mappings and their generalizations, J. Math. Sci. 89 (1998) 1334–1353. [20] J. Mikeš, O. Pokorná, On holomorphically projective mappings onto Kählerian spaces, Rend. Circ. Mat. Palermo 69 (2002) 181–186. [21] J. Mikeš, O. Pokorná, On holomorphically projective mappings onto almost Hermitian spaces, 8th Int. Conf. Opava (2001) 43–48. [22] J. Mikeš, M. Shiha, A. Vanžurová, Invariant objects by holomorphically projective mappings of Kählerian space, 8th Int. Conf. APLIMAT 2009: Conf. Proc. (2009) 439–444. [23] J. Mikeš, N.S. Sinyukov, On quasiplanar mappings of space of affine connection, Sov. Math. 27 (1983) 63–70. [24] J. Mikeš, A. Vanžurová, I. Hinterleitner, Geodesic Mappings and Some Generalizations, Palacky Univ. Press, Olomouc, 2009. [25] J. Mikeš et al, Differential Geometry of Special Mappings, Palacky Univ. Press, Olomouc, 2015. [26] T. Otsuki, Y. Tashiro, On curves in Kaehlerian spaces, Math. J. Okayama Univ. (1954) 57–78. [27] A.Z. Petrov, Simulation of physical fields, Grav. i teor. Otnos., Kazan State Univ. Press, Kazan 4–5 (1968) 7–21. [28] M. Prvanović, Holomorphically projective transformations in a locally product space, Math. Balk. 1 (1971) 195–213. [29] N.S. Sinyukov, Geodesic mappings of Riemannian spaces, Nauka, Moscow, 1979. [30] M. Škodová, J. Mikeš, O. Pokorná, On holomorphically projective mappings from equiaffine symmetric and recurrent spaces onto Kählerian spaces, Rend. Circ. Mat. Palermo 75 (2005) 309–316. [31] M.S. Stanković, M.L. Zlatanović, L.S. Velimirović, Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind, Czech. Math. J. 60 (2010) 635–653. [32] P. Topalov, Geodesic compatibility and integrability of geodesic flows, J. Math. Phys. 44 (2003) 913–929. [33] K. Yano, Differential geometry on complex and almost complex spaces, Pergamon Press, Oxford-London-New York-Paris-Frankfurt, 1965.
utb.fulltext.sponsorship	The paper was supported by project CZ.1.07/2.3.00/30.0035 of Fac. of Appl. Informatics, T. Bata University in Zlín and IGA PrF 2014016 Palacký University Olomouc.
utb.fulltext.projects	CZ.1.07/2.3.00/30.0035
utb.fulltext.projects	IGA PrF 2014016