On the geometry of generalized Robertson-Walker spacetimes: Curvature and Killing fields

Journal of Geometry and Physics

Volumn 31, Issue 1, 1999, Pages 1-15

  Sánchez, Miguel ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

De Sitter spacetime; Generalized Robertson Walker spacetime; Killing fields

Indexed keywords

EID: 0033177192     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(98)00061-8     Document Type: Article

References (18)

1. L.J. Alías, F.J.M. Estudillo, A. Romero, On the Gaussian curvature of maximal surfaces in n-dimensional generalized Robertson-Walker spacetimes, Classical Quantum Gravity 13 (1996) 3211-3219.
2. L.J. Alías, A. Romero, M. Sánchez, Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes, Gen. Relativity Gravitation 27 1 (1995) 71-84.
3. L.J. Alías, A. Romero, M. Sánchez, Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems, Tohôku Math. J. 49 (1997) 337-345.
4. S. Migneni, H.-J. Schmidt, Classification of multidimensional inflationary models, J. Math. Phys. 39 (1998) 998-1010.
5. J.K. Beem, P.E. Ehrlich, K.L. Easley, Global Lorentzian geometry, 2nd ed., Pure Appl. Math., vol. 202, Marcel Dekker, New York, 1996.
6. B. Bishop, O'Neill, Manifolds of Negative Curvature Trans. Am. Math. Soc. 145 (1969) 1-49.
7. J. Carot, J. da Costa, On the geometry of warped spacetimes, Classical Quantum Gravity 10 (1993) 461-482.
8. J. Carot, L.A. Núñez, U. Percoco, Ricci collineations for type B warped spacetimes, Gen. Relativity Gravitation 29 (10) (1997) 1223-1237.
9. V. Daftardar, N. Dadhich: Gradient conformal killing vectors and exact solutions, Gen. Relativity Gravitation 26 (9) (1994) 859-868.
10. R. Deszcz, L. Verstraelen, L. Vrancken, The symmetry of warped product space-times, Gen. Relativity Gravitation 23 (6) (1991) 671-681.
11. B.M. Haddow, J. Carot, Energy-momentum types of warped spacetimes, Classical Quantum Gravity 13 (1996) 289-301.
12. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. I, Tracts in Mathematics, vol. 15, Wiley Interscience, New York, 1963.
13. B. O'Neill, Semi-Riemannian geometry with applications to relativity, Pure Appl. Ser., vol. 103, Academic Press, New York, 1983.
14. A. Romero, M. Sánchez, On the completeness of certain families of semi-Riemannian manifolds, Geom. Dedicata 53 (1994) 103-117.
15. M. Sánchez, Structure of Lorentzian tori with a killing vector field, Trans. Am. Math. Soc. 349 (3) (1997) 1063-1080.
16. M. Sánchez, On the geometry of generalized Robertson-Walker spacetimes: Geodesics, Gen. Relativity Gravitation 30 (6) (1998) 915-932.
17. Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Am. Math. Soc. 117 (1965) 251-275.
18. H. Wu, On the de Rham decomposition theorem, Illinois J. Math. 8 (1964) 291-311.