Geodesic
On the Riemann extension of the G\"odel space-time metric
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 43-62.

Voir la notice de l'article provenant de la source Math-Net.Ru

Some properties of the Gödel space-metric and its Riemann extension are studied. The spectrum of de Rham operator acting on 1-forms is studied. The examples of translation surfaces of the Gödel space-metric are constructed. 
@article{BASM_2005_3_a4,
     author = {Valery Driuma},
     title = {On the {Riemann} extension of the {G\"odel} space-time metric},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {43--62},
     publisher = {mathdoc},
     number = {3},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2005_3_a4/}
}
TY  - JOUR
AU  - Valery Driuma
TI  - On the Riemann extension of the G\"odel space-time metric
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2005
SP  - 43
EP  - 62
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2005_3_a4/
LA  - en
ID  - BASM_2005_3_a4
ER  - 
%0 Journal Article
%A Valery Driuma
%T On the Riemann extension of the G\"odel space-time metric
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2005
%P 43-62
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2005_3_a4/
%G en
%F BASM_2005_3_a4
Valery Driuma. On the Riemann extension of the G\"odel space-time metric. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 43-62. http://geodesic.mathdoc.fr/item/BASM_2005_3_a4/

[1] Paterson E. M., Walker A. G., “Riemann extensions”, Quart. J. Math. Oxford, 3 (1952), 19–28 | DOI | MR

[2] Dryuma V., “Applications of Riemannian and Einstein-Weyl Geometry in the theory of second order ordinary differential equations”, Theoretical and Mathematical Physics, 128:1 (2001), 845–855 | DOI | MR | Zbl

[3] Dryuma V., “The Riemann Extension in theory of differential equations and their applications”, Matematicheskaya fizika, analiz, geometriya, 10:3 (2003), 1–19 | MR

[4] Dryuma V., “The Invariants, the Riemann and Einstein-Weyl geometry in theory of ODE's and all that”, New Trends in Integrability and Partial Solvability, eds. A. B. Shabat et al., Kluwer Academic Publishers, 2004, 115–156 ; , 11 March, 2003, p. 1–37 ArXiv: nlin: SI/0303023 | MR | Zbl

[5] Dryuma V., “The Riemann Extension of the Schwarzschild space-time”, Buletinul A. Ş. M., Matematica, 2003, no. 3(43), 92–103 | MR

[6] Dryuma V., “On geodesical extension of the Schwarzshild space-time”, Proceedings of Institute of Mathematics of NAS of Ukraine, 50 (2004), 1294–1300 | MR | Zbl

[7] Dryuma V., “On the Riemann extension of the space-time with vanishing curvature invariants”, ECM'2004 (Sweden, Stockholm, June 27–July 2)

[8] Dryuma V., The Riemann Extension of the Minkowsky space-time in rotating coordinate system, , v. 1, 24 May 2005, p. 1–10 ArXiv: gr-qc/0505122 | MR

[9] Dryuma V., On theory of the spaces of constant curvature, , 18 May 2005, p. 1–12 ArXiv: math.DG/0505376 | MR

[10] Dryuma V., Riemann extensions in theory of the first order systems of differential equations, , 25 October 2005, p. 1–21 ArXiv: math.DG/0510526 | MR

[11] Dryuma V., “From the Number theory to the Riemann geometry”, Scientific Papers International Conference “Differential Equations and Computer Algebra Systems (DE and CAS'2005)”, Part 1, BGPU, Minsk, 2005, 14–15

[12] Hawking S. W., Ellis G., The Large Scale Structure of Space-Time, Moskow, 1977 (in Russian) | Zbl

[13] Dautcourt G., Abdel-Megied M., Revisiting the Light Cone of the Gödel Universe, , 3 Nov 2005, p. 1–23 ArXiv: gr-qc/0511015 | MR

[14] Jackiw R., A Pure Cotton Kink in a Funny Place, , v. 2, 21 July 2004 ArXiv: math-ph/0403044

[15] Eisenhart L. P., Riemannian geometry, Moskow, 1948 (in Russian) | MR

[16] Elianu I. P., “Cercetari asupra sistemelor de ecuatii lineare cu derivate partiale de tip Laplace”, Studii si cercetari matematice, IV:1–2 (1953), 155–196 | MR