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2018 | 107 | 31-45
Article title

Spacetimes embedded into E6

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Abstracts
EN
We study the local and isometric embedding of Riemannian spacetimes into the pseudo-Euclidean flat E6. Our main purpose is to pinpoint the known results with the corresponding references, and to indicate the main routes and connections from here to the still open problems in the field. Some new results are also included in order to round off our discussion.
Discipline
Year
Volume
107
Pages
31-45
Physical description
Contributors
  • Centro de Investigación en Computación, Instituto Politécnico Nacional, CDMX, México
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Col. Lindavista 07738, CDMX, México
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Col. Lindavista 07738, CDMX, México
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Col. Lindavista 07738, CDMX, México
References
  • [1] D. Kramer, H. Stephani, M. Mac Callum, E. Hertl, Exact solutions of Einstein field equations, Cambridge University Press (1980).
  • [2] H. F. Goenner, General relativity and gravitation, Ed. A. Held, vol. I, Chap. 14, Plenum New York (1980).
  • [3] C. Fronsdal, Rev. Mod. Phys. 37 (1965) 221.
  • [4] Y. Ne’eman, Rev. Mod. Phys. 37 (1965) 227.
  • [5] T. H. Phát, Acta Phys. Polon. B2 (1971) 567.
  • [6] B. M. Barbashov, V. V. Nesterenko, Forts. der Physik 28 (1980) 427.
  • [7] A. Z. Petrov, Recent developments in general relativity, Pergamon Press, Oxford (1962) 382-384.
  • [8] J. L. Synge, Comm. Dublin Inst. Adv. Stud. Serie A, No. 15 (1964).
  • [9] G. Ludwig, Am. J. Phys. 37 (1969) 1225.
  • [10] R. A. D’Inverno, R. A. Russell-Clark, J. Math. Phys. 12 (1971) 1258.
  • [11] G. Ares de Parga, O. Chavoya, J. López-Bonilla, G. Ovando, Rev. Mex. Fis. 35 (1989) 201.
  • [12] V. Gaftoi, J. López-Bonilla, J. Morales, G. Ovando, J.J. Peña, J. Moscow Phys. Soc. 6 (1996) 267.
  • [13] J. Plebañski, Acta Phys. Polon. 26 (1964) 963.
  • [14] J. Plebañski, J. Stachel, J. Math. Phys. 9 (1968) 269.
  • [15] H. F. Goenner, J. Stachel, J. Math. Phys. 11 (1970) 3358.
  • [16] A. Barnes, Gen. Rel. Grav. 5 (1974) 147.
  • [17] C. B. G. McIntosh, J. M. Foyster, A. W. C. Lun, J. Math. Phys. 22 (1981) 2620.
  • [18] H. N. Núñez-Yépez, J. López-Bonilla, A. L. Salas-Brito, J.M. Rivera, Acta Phys. Slovaca 46 (1996) 87.
  • [19] K. R. Karmarkar, Proc. Indian Acad. Sci. A27 (1948) 56.
  • [20] K. P. Singh, S.N. Pandey, Proc. Indian Acad.Sci. A26 (1960) 665.
  • [21] J. Plebañski, Bull. Acad. Polon. Sci. 9 (1962) 373.
  • [22] J. Rosen, Rev. Mod. Phys. 37 (1965) 204.
  • [23] H. Stephani, Commun. Math. Phys. 4 (1967) 137.
  • [24] H. Stephani, Commun. Math. Phys. 5 (1967) 337.
  • [25] C. D. Collinson, J. Math. Phys. 9 (1968) 403.
  • [26] J. Goldman, N. Rosen, Gen. Rel. Grav. 2 (1971) 367.
  • [27] R. S. Tikekar, Curr. Sci. 39 (1971) 460.
  • [28] J. Krishna Rao, Gen. Rel. Grav. 3 (1971) 211.
  • [29] G. P. Pokhariyal, Gen. Rel. Grav. 3 (1972) 87.
  • [30] Y. K. Gupta, P. Goel, Gen. Rel. Grav. 19 (1975) 499.
  • [31] D. E. Hodgkinson, Gen. Rel. Grav. 19 (1987) 253.
  • [32] O. Chavoya, J. Fernández, D. Ladino, J. López-Bonilla, Rev. Colomb. Fis. 23 (1991) 15.
  • [33] R. H. Boyer, J. Plebanski, Rev. Mex. Fis. 39 (1993) 870.
  • [34] N. Van Der Bergh, Class. Quantum Grav. 13 (1996) 2817 and 2839.
  • [35] E. T. Newman, R. Penrose, J. Math. Phys. 3 (1962) 566.
  • [36] C. D. Collinson, J. Math. Phys. 7 (1966) 608.
  • [37] G. Ares de Parga, J. López-Bonilla, G. Ovando, T. Matos, Rev. Mex. Fis. 35 (1989) 393.
  • [38] D. Ladino, J. López-Bonilla, Rev. Mex. Fis. 35 (1989) 623.
  • [39] P. Szekeres, Nuovo Cim. A43 (1966) 1062.
  • [40] P. Greenberg, Stud. Appl. Math. 51 (1972) 415.
  • [41] M. Sh. Yakupov, Grav. Teor. Otnos. Univ. Kazan 9 (1973) 109.
  • [42] H. F. Goenner, Habilitation Lecture, Göttingen Universität (1973).
  • [43] T. Y. Thomas, Acta Math. 67 (1936) 169.
  • [44] R. Fuentes, J. López-Bonilla, G. Ovando, T. Matos, Gen. Rel. Grav. 21 (1989) 277.
  • [45] C. D. Collinson, Commun. Math. Phys. 8 (1968) 1.
  • [46] H. F. Goenner, Gen. Rel. Grav. 8 (1977) 139.
  • [47] M. Matsumoto, J. Math. Soc. Jpn. 2 (1950) 67.
  • [48] V. Gaftoi, J. López-Bonilla, D. Navarrete, G. Ovando, Rev. Mex. Fis. 36 (1990) 503.
  • [49] C. Lanczos, Ann. Math. 39 (1938) 842.
  • [50] C. Lanczos, Rev. Mod. Phys. 34 (1962) 379.
  • [51] M. Sh. Yakupov, Sov. Phys. Doklady (Eng. Transl.) 13 (1968) 585.
  • [52] R. P. Kerr, Phys. Rev. Lett. 11 (1963) 237.
  • [53] B. Léauté, Ann. Inst. Henri Poincaré A8 (1968) 93.
  • [54] M. M. Schiffer, R. J. Alder, J. Mark, Ch. Sheffield, J. Math. Phys. 14 (1973) 52.
  • [55] S. Chandrasekhar, The mathematical theory of black holes, Oxford Univesity Press (1983).
  • [56] V. Gaftoi, J. López-Bonilla, J. Morales, D. Navarrete, G. Ovando, Rev. Mex. Fis. 36 (1990) 498.
  • [57] J. Plebañski, private communication.
  • [58] K. Gödel, Rev. Mod. Phys. 21 (1949) 447.
  • [59] K. Eguchi, J. Math. Tokushima Univ. 1 (1967) 17.
  • [60] D. Ladino, J. López-Bonilla, J. Morales, G. Ovando, Rev. Mex. Fis. 36 (1990) 498.
  • [61] G. González, J. López-Bonilla, M. Rosales, Pramana J. Phys. 42 (1994) 85.
  • [62] J. López-Bonilla, J. Morales, M. Rosales, Braz. J. Phys. 24 (1994) 522.
  • [63] N. Van der Bergh, private communication.
  • [64] J. López-Bonilla, G. Ovando, J. Rivera, Aligarh Bull. Math. 17 (1997-98) 63.
  • [65] D. E. Hodgkinson, Gen. Rel. Grav. 16 (1984) 569.
  • [66] J. Plebañski, Bull. Acad. Polon. Sci. 9 (1961) 587.
  • [67] R. Penney, J. Math. Phys. 5 (1964) 1431.
  • [68] E. Piña, Rev. Mex. Fis. 16 (1967) 233.
  • [69] J. López-Bonilla, Rev. Colomb.Fis. 17 (1985) 1.
  • [70] C. N. Kozameh, E. T. Newman, K. P. Tod, Gen. Rel. Grav. 17 (1985) 343.
  • [71] R. Penrose, Ann. Phys. 10 (1960) 171.
  • [72] S. J. Campbell, J. Wainwright, Gen Rel. Grav. 8 (1977) 987.
  • [73] H. F. Goenner, Gen. Rel. Grav. 6 (1975) 75.
  • [74] H. F. Goenner, private communication.
  • [75] E. Kasner, Am. J. Math. 43 (1921) 130.
  • [76] C. Fronsdal, Phys. Rev. 116 (1959) 778.
  • [77] P. Calva, J. López-Bonilla, G. Ovando, J. Bangladesh Acad. Sci. 24 (2000) 239.
  • [78] J. H. Caltenco, J. López-Bonilla, J. Morales, G. Ovando, Chinese J. Phys. 39 (2001) 397.
  • [79] W. Kinnersley, J. Math. Phys. 10 (1969) 1995.
  • [80] J. López-Bonilla, G. Ovando, J. Rivera, Aligarh Bull. Math. 18 (1999) 39.
  • [81] A. H. Taub, Ann. Math. 53 (1971) 472.
  • [82] E. Kasner, Am. J. Math. 43 (1921) 217.
  • [83] S. T. C. Siklos, Algebraically special homogeneous space-times, preprint, Oxford University (1978).
  • [84] A. Held, Lett. Nuovo Cim. 11 (1974) 545.
  • [85] I. Robinson, Gen. Rel. Grav. 6 (1974) 423.
  • [86] J. López-Bonilla, G. Ovando, J. J. Peña, Found. Phys. Lett. 12 (1999) 401.
  • [87] I. Hauser, Phys. Rev. Lett. 33 (1974) 1112.
  • [88] V. Gaftoi, J. López-Bonilla, G. Ovando, Bull. Allahabad Math. Soc. 18 (2003) 35.
  • [89] J. López-Bonilla, G. Ovando, Gen. Rel. Grav. 31 (1999) 1071.
  • [90] H. F. Goenner, Tensor New Series 30 (1976) 15.
  • [91] J. López-Bonilla, J. Rivera, H. Yee-Madeira, Braz. J. Phys. 25 (1995) 80.
  • [92] J. López-Bonilla, H. N. Núñez-Yépez, Pramana J. Phys. 46 (1996) 87.
  • [93] D. E. Hodgkinson, J. Math. Phys. 42 (2001) 863.
Document Type
article
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YADDA identifier
bwmeta1.element.psjd-de907adf-946a-4af0-9add-926fbdc645ea
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