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2024 | OriginalPaper | Chapter

On General Solutions of Sinyukov Equations on Two-Dimensional Equidistant (pseudo-)Riemannian Spaces

Authors : Patrik Peška, Lenka Vítková, Josef Mikeš, Irina Kuzmina

Published in: Differential Geometric Structures and Applications

Publisher: Springer Nature Switzerland

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Abstract

The paper is devoted to study of Sinyukov equations on two-dimensional equidistant (pseudo-) Riemannian spaces. The general solution of Sinyukov equations is found beyond these spaces under minimal requirements for the differentiability of the studied objects.

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Bondi, H. et al.: Rival theories of cosmology. A symposium and discussion of modern theories of the structures of the universe. Oxford University Press (1960)

Brinkmann, H.W.: Einstein spaces which mapped conformally on each other. Math. Ann. 94 (1925)

Chepurna, O., Hinterleitner, I.: On the mobility degree of (pseudo-) Riemannian spaces with respect to concircular mappings. Miskolc Math. Notes 14:2, 561–568 (2013)MathSciNetCrossRef

Ćirić, M.S., Zlatanović, M.Lj.; Stanković, M.S., Velimirović, L.S.: On geodesic mappings of equidistant generalized Riemannian spaces. Appl. Math. Comput. 218:12, 6648–6655 (2012)

Eisenhart, L.P.: Non-Riemannian geometry. Reprint of the 1927 original. Mineola, NY: Dover Publ. (2005)

Fialkow, A.: Conformals geodesics. Trans. AMS 45, 443–473 (1939)MathSciNetCrossRef

Gorbatyi, E.Z.: On geodesic mapping of equidistant Riemannian spaces and first class spaces. Ukr. Geom. Sb. 12, 45–53 (1972)MathSciNet

Hall, G.: Four-Dimensional Manifolds and Projective Structure. New York etc.: CRC Press (2023)CrossRef

Hinterleitner, I.: Conformally-projective harmonic mappings of equidistant manifolds with the Friedmann models as example. Proc. 6th Int. Conf. Aplimat, 97–102 (2007)

10.

Hinterleitner, I.: Conformally-projective harmonic diffeomorphisms of equidistant manifolds. R. Soc. Mat. Esp. 11, 298–303 (2007)MathSciNet

11.

Hinterleitner, I.: Selected special vector fields and mappings in Riemannian geometry. J. Appl. Math. 1:2, 30–37 (2008)

12.

Hinterleitner, I.: Special mappings of equidistant spaces. J. Appl. Math. 2, 31–36 (2008)

13.

Hinterleitner, I.: Special mappings of equidistant spaces. Vědecké spisy VUT Brno. Edice Ph.D. Thesis, 525, 20p. (2009)

14.

Hinterleitner, I.: Geodesic mappings on compact Riemannian manifolds with conditions on sectional curvature. Publ. Inst. Math. 94 (108), 125–130 (2013)MathSciNetCrossRef

15.

Hinterleitner, I., Mikeš, J.: Geodesic mappings of (pseudo-)Riemannian manifolds preserve class of differentiability. Miskolc Math. Notes 14:2, 575–582 (2013)MathSciNetCrossRef

16.

Hinterleitner, I., Berezovski, V., Chepurna, E., Mikeš, J.: On the concircular vector fields of spaces with affine connection. Acta Math. Acad. Paedagog. Nyházi. (N.S.) 33:1, 53–60 (2017)

17.

Hinterleitner, I., Mikeš, J.: Geodesic mappings onto Riemannian manifolds and differentiability. Geometry, Integrability and Quantization 18, 183–190 (2017)MathSciNetCrossRef

18.

Hinterleitner, I., Berezovski, V., Chepurna, E., Mikeš, J.: On the concircular vector fields of spaces with affine connection. Acta Math. Acad. Paedagog. Nyházi. (N.S.) 33:1, 53–60 (2017)

19.

Kagan, V.F.: Subprojective spaces. Bibl. Russkoi Nauki, Moscow (1961)

20.

Kühnel, W., Rademacher, H.-B.: Conformal diffeomorphisms preserving the Ricci tensor. Proc. AMS 123:9, 2841–2848 (1995)MathSciNetCrossRef

21.

Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci. (New York) 78:3, 311–333 (1996)MathSciNetCrossRef

22.

Mikeš, J.: Geodesic mappings of semisymmetric Riemannian spaces. Odessk. Univ. Moscow: Archives at VINITI, No. 3924-76, 19 p. (1976)

23.

Mikeš, J.; Equidistant Kähler spaces. Math. Notes 38:4, 855–858 (1985)MathSciNetCrossRef

24.

Mikeš, J.: On Sasaki spaces and equidistant Kähler spaces. Sov. Math. Dokl. 34, 428–431 (1987)

25.

Mikeš, J., Starko, G.A.: Hyperbolically Sasakian and equidistant hyperbolically Kählerian spaces. J. Sov. Math. 59:2, 756–760 (1992)CrossRef

26.

Mikeš, J.: Holomorphically projective mappings and their generalizations. J. Math. Sci. (New York) 89:3, 1334–1353 (1998)MathSciNetCrossRef

27.

Mikeš, J., Rachůnek, L.: $T$-semisymmetric spaces and concircular vector fields. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 69, 187–193 (2002)

28.

Mikeš, J. et al.: Differential geometry of special mappings. 2th ed. Palacky Univ. Press, Olomouc (2019)CrossRef

29.

Moldobayev, Dz.: Special transformations of Riemannian spaces, which preserved Einstein tensor. Ph.D. Thesis, Bishkek Univ. 1986

30.

Najdanović, M.S., Zlatanović, M.Lj., Hinterleitner, I.: Conformal and geodesic mappings of generalized equidistant spaces. Publ. Inst. Math., Nouv. Sér. 98 (112), 71–84 (2015)

31.

Najdanović M.S.: On the problem of geodesic mappings and deformations of generalized Riemannian spaces. J. Math. Anal. Appl. 452:1, 634–645 (2017)MathSciNetCrossRef

32.

Peška, P., Mikeš, J., Rýparová, L., Chepurna, O.: On general solutions of equidistant vector fields on two-dimensional (pseudo-) Riemannian spaces. Filomat 37:25, 8569–8574 (2023)MathSciNet

33.

Rýparová, L., Mikeš, J.: On geodesic bifurcations. Geom., Integrability, Quantization 18, 217–224 (2017)

34.

Rýparová, L., Mikeš, J., Sabykanov, A.: On geodesic bifurcations of product spaces. J. Math. Sci., New York 239, No. 1, 86–91 (2019)

35.

Sinyukov, N.S.: On geodesic mappings of Riemannian manifolds onto symmetric spaces. Dokl. Akad. Nauk SSSR 98, 21–23 (1954)MathSciNet

36.

Sinyukov, N.S.: On equidistant spaces. Vestn. Odessk. Univ., Odessa, 133–135 (1957)

37.

Sinyukov, N.S.: Geodesic mappings of Riemannian spaces. Nauka, Moscow (1979)

38.

Shandra, I.G.: Geodesic mappings of equidistant spaces and Jordan algebras of spaces $V_n(K)$. Diff. geom. mnogoobr. figur, Kaliningrad, 104–111 (1993)

39.

Shandra, I.G.: On concircular tensor fields and geodesic mappings of pseudo-Riemannian spaces. Russ. Math. 45:1, 52–62 (2001)MathSciNet

40.

Shandra, I.G.: Concircular vector fields on semi-Riemannian spaces. J. Math. Sci., New York 142:5, 2419–2435 (2007)

41.

Shandra I. G., Mikeš, J.: Geodesic mappings of $V_n(K)$-spaces and concircular vector fields. Mathematics 7(8), 692 (2019)CrossRef

42.

Shapiro, Ya.L.: Geodesic fields of directions and projective systems of paths. Mat. Sb. (N.S.) 36(78), 125–148 (1955)

43.

Shirokov, P.A.: Selected investigations on geometry. Kazan Univ. Press (1966)

44.

Shiha, M., Mikeš, J.: On equidistant, parabolically Kählerian spaces. Tr. Geom. Semin. 22, 97–107 (1994)

45.

Shulikovskij, V.I.: Invariant criterium of Liouvill surfaces. Dokl. AN SSSR 94:1, 29–32, 1954

46.

Sinyukov, N.S.: A contribution to the theory fo geodesic mapping of Riemannian spaces. Sov. Math., Dokl. 7, 1004–1006 (1966)

47.

Vagner, V.: On the problem of determining the invariant characteristics of Liouville surfaces. Tr. Semin. Vektorn. Tenzorn. Anal. 5, 246–249 (1941)MathSciNet

48.

Vries, H.L:. Über Riemannsche Räume, die infinitesimal konforme Transformationen gestatten. Math. Z. 60:3, 328–347 (1954)

49.

Yano, K.: On the torse-forming directions in Riemannian spaces. Proc. Imp. Acad. Tokyo 20, 340–345 (1944)MathSciNet

50.

Yano, K.: Concircular geometry. Proc. Imp. Acad. Tokyo, 16, 195–200, 354–360, 442–448, 505–511 (1940)

51.

Zajtsev, V.F., Polyanin, A.D.: Handbook of ordinary differential equations. (Spravochnik po obyknovennym differentsial’nym uravneniyam.) Moscow: Fizmatlit. (2001)

52.

Zlatanović, M., Hinterleitner, I., Najdanović, M.: On equitorsion concircular tensors of generalized Riemannian spaces. Filomat 28:3, 463–471 (2014)

Title: On General Solutions of Sinyukov Equations on Two-Dimensional Equidistant (pseudo-)Riemannian Spaces
Authors: Patrik Peška
Lenka Vítková
Josef Mikeš
Irina Kuzmina
Publisher: Springer Nature Switzerland
Book: Differential Geometric Structures and Applications
Print ISBN: 978-3-031-50585-0

Electronic ISBN: 978-3-031-50586-7

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-50586-7_9

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