For the Riemannian space Vn, the invariantly associated with Vn space V˜n2 is constructed, which implements a second order approximation for Vn. We studied conformal transformations when the original space is a space of non-zero constant curvature.

Topics
Conformal differential geometry, Perturbation theory
1.
L.P.
 
Eisenhart
,
Continuous Transformation Groups
(
FLPH
,
Moscow
,
1947
). [un Russian]
Google Scholar
 
2.
L.
 
Evtushik
,
V.
 
Kiosak
, and
J.
 
Mikesh
 (
2010
)
The mobility of Riemannian spaces with respect to conformal mappings onto Einstein spaces
”,
Russian Mathematics
 
54
(
8
),
29
–
33
.
https://doi.org/10.3103/S1066369X10080049
Google Scholar
Crossref
Search ADS
 
3.
V.F.
 
Kahan
,
Subprojective Spaces
(
Fizmatgiz
,
Moscow
,
1961
). [in Russian]
Google Scholar
 
4.
V.
 
Kiosak
,
O.
 
Lesechko
, and
O.
 
Savchenko
, “
Mappings of spaces with affine connection
,” in
17th Conference on Applied Mathematics, APLIMAT 2018 - Procedings
(
Bratislava
,
2018
), pp.
563
–
569
.
Google Scholar
 
5.
V.
 
Kiosak
 and
V.
 
Matveev
 (
2014
)
There exist no 4-dimensional geodesically equivalent metrics with the same stress-energy tensor
,
Journal of Geometry and Physics
 
78
,
1
–
11
.
https://doi.org/10.1016/j.geomphys.2014.01.002
Google Scholar
Crossref
Search ADS
 
6.
V.A.
 
Kiosak
,
V.S.
 
Matveev
, and
I.G.
 
Shandra
 (
2010
)
On the degree of geodesic mobility for Riemannian metrics
,
Mathematical Notes
 
87
(
3-4
),
586
–
587
.
https://doi.org/10.1134/S0001434610030375
Google Scholar
Crossref
Search ADS
 
7.
V. A.
 
Kiosak
 (
2012
)
On the conformal mappings of quasi-Einstein spaces
,
Journal of Mathematical Sciences
 
184
,
12
–
18
.
https://doi.org/10.1007/s10958-012-0848-6
Google Scholar
Crossref
Search ADS
 
8.
V.
 
Kiosak
,
O.
 
Savchenko
, and
T.
 
Shevchenko
, “
Holomorphically Projective Mappings of Special Kahler Manifolds,” in
 
AMiTaNS’18
,
AIP
CP
202c
, edited by
M.D.
 
Todorov
 (
American Institute of Physics
,
Melville, NY
,
2018
), paper
08004
.
Google Scholar
Crossref
Search ADS
 
9.
V.
 
Kiosak
 and
I.
 
Hinterleitner
 (
2010
)
Special Einstein’s equations on Kahler manifolds
,
Archivum Mathematicum
 
46
(
5
),
333
–
337
.
Google Scholar
 
10.
V.
 
Kiosak
 and
I.
 
Hinterleitner
, “(Ric)-Vector Fields on Conformally Flat Spaces,” in
AIP CP
 
1191
(
American Institute of Physics
,
Melville, NY
,
2009
), pp.
98
–
103
.
Google Scholar
 
11.
A.Z.
 
Petrov
,
New Methods in General Theory of Relativity
(
Nauka
,
Moscow
,
1966
). [in Russian]
Google Scholar
 
12.
S.M.
 
Pokas
, “
Infinitely small conformal transformations in the Riemannian space of the second approximation
,” in
Proc. of the Intern. Geom. Center
 
7
(
2014
), pp.
36
–
50
.
Google Scholar
 
13.
S.M.
 
Pokas
 (
2011
)
Lie groups of motions in the Riemannian space of the second approximation
,
Journal of the Penza State Pedagogical Univ. n. aft. V.G. Belinsky
 
6
, pp.
173
–
183
.
Google Scholar
 
14.
S.M.
 
Pokas
,
A.V.
 
Krutoholova
, and
L.G.
 
Tsehmeystruk
 (
2014
)
Induced mappings of Riemannian spaces of second approximation
,
Math Studios (Lviv)
 
41
,
220
–
224
.
Google Scholar
 
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