On some exact solutions of heavenly equations in four dimensions
Source abstract
Abstract
Some new classes of exact solutions (so-called functionally invariant solutions) of the elliptic and hyperbolic complex Monge–Ampère equations and of the second heavenly equation are found. Besides, non-invariance of the found classes of solutions of the hyperbolic complex Monge–Ampère equation and the second heavenly equation is investigated—these classes of solutions determine the new classes of metrics without Killing vectors. A criterion of non-invariance of the solutions belonging to the found classes is also formulated.
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Research context
OpenAlex topics: Nonlinear Waves and Solitons · Geometry and complex manifolds · Geometric Analysis and Curvature Flows
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Affiliations
The Pedagogical University of Cracow , ul. Podchorążych 2, 30-084 Kraków, Poland
Funding
Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie · The Pedagogical University of Cracow
References (66)
Show source-provided references
1. 2001
2. Phys. Rev. · 1968 · 167 · 117510.1103/physrev.167.1175 ↗
3. 2005
4. J. Math. Phys. · 1975 · 16 · 239510.1063/1.522505 ↗
5. J. Math. Phys. · 1989 · 30 · 108110.1063/1.528379 ↗
6. Phys. Lett. A · 2007 · 369 · 29910.1016/j.physleta.2007.04.100 ↗
7. J. Phys. A: Math. Gen. · 2004 · 37 · 752710.1088/0305-4470/37/30/010 ↗
8. J. Phys. A: Math. Theor. · 2007 · 40 · 937110.1088/1751-8113/40/31/014 ↗
9. Phys. Lett. A · 2006 · 359 · 61310.1016/j.physleta.2006.07.011 ↗
10. Boll. Un. Mat. Ital. A · 1978 · 15 · 197
11. Banach Cent. Publ. · 2017 · 113 · 27510.4064/bc113-0-15 ↗
12. Phys. At. Nucl. · 2007 · 70 · 58410.1134/s1063778807030209 ↗
13. J. Nonlinear Math. Phys. · 2008 · 15 · 38510.2991/jnmp.2008.15.s3.37 ↗
14. J. Nonlinear Math. Phys. · 2008 · 15 · 41710.2991/jnmp.2008.15.s3.40 ↗
15. Phys. Lett. A · 1977 · 60 · 8110.1016/0375-9601(77)90386-3 ↗
16. J. Phys. A: Math. Gen. · 2003 · 36 · 1002310.1088/0305-4470/36/39/304 ↗
17. Classical Quantum Gravity · 1997 · 14 · L5910.1088/0264-9381/14/3/004 ↗
18. 2010
19. Commun. Anal. Geom. · 2008 · 16 · 43710.4310/cag.2008.v16.n2.a5 ↗
20. Ukr. Math. J. · 1996 · 48 · 77510.1007/bf02384226 ↗
21. Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki · 2009 · 151 · 60
22. J. Geom. Phys. · 2010 · 60 · 160410.1016/j.geomphys.2010.05.009 ↗
23. Mem. Am. Math. Soc. · 2005 · 178 · 84010.1090/memo/0840 ↗
24. Z. Kuznetsova, Z. Popowicz, and F. Toppan, J. Phys. A: Math. Gen. 38, 7773 (2005); arXiv:hep-th/0504214. 10.1088/0305-4470/38/35/01110.1088/0305-4470/38/35/011 ↗
25. Czech J. Phys. · 2004 · 54 · 138710.1007/s10582-004-9806-y ↗
26. Proc. Rom. Acad., Ser. A · 2016 · 17 · 210
27. J. Phys. A: Math. Theor. · 2009 · 42 · 39520210.1088/1751-8113/42/39/395202 ↗
28. Classical Quantum Gravity · 2006 · 23 · 490710.1088/0264-9381/23/15/010 ↗
29. Phys. Rev. Lett. · 1994 · 72 · 80010.1103/physrevlett.72.800 ↗
30. Phys. Lett. A · 1993 · 181 · 43510.1016/0375-9601(93)91145-u ↗
31. Phys. Lett. A · 1996 · 212 · 2210.1016/0375-9601(96)00025-4 ↗
32. J. Math. Phys. · 1977 · 18 · 102210.1063/1.523363 ↗
33. Acta Phys. Pol., B · 1995 · 26 · 889
34. A. A. Malykh and M. B. Sheftel, J. Phys. A: Math. Theor. 44, 155201 (2011); arXiv:1011.2479. 10.1088/1751-8113/44/15/15520110.1088/1751-8113/44/15/155201 ↗
35. 1994
36. J. Comput. Appl. Math. · 2010 · 233 · 160710.1016/j.cam.2009.02.075 ↗
37. Acta Phys. Pol., A · 1984 · 65 · 457
38. J. Phys. A: Math. Gen. · 2002 · 35 · 615710.1088/0305-4470/35/29/315 ↗
39. Mityushev · 2015 · 27310.1007/978-3-319-12577-0 ↗
40. Ł. T. Stȩpień, arXiv:1208.2905 (2012).
41. Travaux Inst. Physico–Math. Stekloff, Acad. Sci. · 1934 · 5 · 259
42. CR (Doklady) Acad. Sci. URSS (NS) · 1944 · 42 · 371
43. Differ. Uravn. · 1981 · 17 · 853
44. 2005
45. Dokl. Akad. Nauk SSSR · 1972 · 205 · 30
46. Differ. Uravn. · 1975 · 11 · 533
47. Gerdjikov · 2009 · 210
48. Symmetry, Integrability Geom.: Methods Appl. · 2011 · 7 · 04310.3842/SIGMA.2011.043 ↗
49. 1983
50. Wojtasiewicz · 1973
51. Pei Dang · 2017 · 32710.1007/978-3-319-48812-7 ↗
52. Acta Phys. Pol., B · 1994 · 25 · 1079
53. Funct. Anal. Appl. · 1979 · 13 · 16610.1007/bf01077483 ↗
54. 1993
55. Wójcik · 1998 · 81
56. J. Phys. A: Math. Gen. · 2002 · 35 · 34310.1088/0305-4470/35/2/312 ↗
57. 2004
58. 1986
59. 2012
60. 2012
61. Rom. Rep. Phys. · 2013 · 65 · 1155
62. World Appl. Sci. J. · 2013 · 24 · 94410.5829/idosi.wasj.2013.24.07.1041 ↗
63. Appl. Math. Comput. · 2015 · 269 · 36310.1016/j.amc.2015.07.060 ↗
64. Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki · 2017 · 27 · 35510.20537/vm170306 ↗
65. J. Math. Phys. · 2003 · 44 · 343010.1063/1.1588466 ↗
66. On some exact solutions of elliptic Monge-Ampère equation