Acknowledgement
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11761061, 11261051).
References
- N. Abe, N. Koike, and S. Yamaguchi, Congruence theorems for proper semi-Riemannian hypersurfaces in a real space form, Yokohama Math. J. 35 (1987), no. 1-2, 123-136.
- K. Akutagawa, On spacelike hypersurfaces with constant mean curvature in the de Sitter space, Math. Z. 196 (1987), no. 1, 13-19. https://doi.org/10.1007/BF01179263
- L. J. Alias, A. Romero, and M. Sanchez, Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems, Tohoku Math. J. (2) 49 (1997), no. 3, 337-345. https://doi.org/10.2748/tmj/1178225107
- J. O. Baek, Q.-M. Cheng, and Y. J. Suh, Complete space-like hypersurfaces in locally symmetric Lorentz spaces, J. Geom. Phys. 49 (2004), no. 2, 231-247. https://doi.org/10.1016/S0393-0440(03)00090-1
- A. Brasil, Jr., A. G. Colares, and O. Palmas, A gap theorem for complete constant scalar curvature hypersurfaces in the de Sitter space, J. Geom. Phys. 37 (2001), no. 3, 237-250. https://doi.org/10.1016/S0393-0440(00)00046-2
- E. Calabi, Examples of Bernstein problems for some nonlinear equations, in Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968), 223-230, Amer. Math. Soc., Providence, RI, 1970.
- B.-Y. Chen, Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011. https://doi.org/10.1142/9789814329644
- S. Y. Cheng and S. T. Yau, Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces, Ann. of Math. (2) 104 (1976), no. 3, 407-419. https://doi.org/10.2307/1970963
- S. M. Choi, S. M. Lyu, and Y. J. Suh, Complete space-like hypersurfaces in a Lorentz manifold, Math. J. Toyama Univ. 22 (1999), 53-76.
- H. K. El-Sayied, S. Shenawy, and N. Syied, On symmetries of generalized Robertson-Walker spacetimes and applications, J. Dyn. Syst. Geom. Theor. 15 (2017), no. 1, 51-69. https://doi.org/10.1080/1726037X.2017.1323418
- A. J. Goddard, Some remarks on the existence of spacelike hypersurfaces of constant mean curvature, Math. Proc. Cambridge Philos. Soc. 82 (1977), no. 3, 489-495. https://doi.org/10.1017/S0305004100054153
- T. Ishihara, Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature, Michigan Math. J. 35 (1988), no. 3, 345-352. https://doi.org/10.1307/mmj/1029003815
- U.-H. Ki, H.-J. Kim, and H. Nakagawa, On space-like hypersurfaces with constant mean curvature of a Lorentz space form, Tokyo J. Math. 14 (1991), no. 1, 205-216. https://doi.org/10.3836/tjm/1270130500
- D.-S. Kim and Y. H. Kim, Compact Einstein warped product spaces with nonpositive scalar curvature, Proc. Amer. Math. Soc. 131 (2003), no. 8, 2573-2576. https://doi.org/10.1090/S0002-9939-03-06878-3
- O. Kowalski, Generalized symmetric spaces, Lecture Notes in Mathematics, 805, Springer-Verlag, Berlin, 1980.
- S. Montiel, An integral inequality for compact spacelike hypersurfaces in de Sitter space and applications to the case of constant mean curvature, Indiana Univ. Math. J. 37 (1988), no. 4, 909-917. https://doi.org/10.1512/iumj.1988.37.37045
- S. Montiel, A characterization of hyperbolic cylinders in the de Sitter space, Tohoku Math. J. (2) 48 (1996), no. 1, 23-31. https://doi.org/10.2748/tmj/1178225410
- M. Okumura, Hypersurfaces and a pinching problem on the second fundamental tensor, Amer. J. Math. 96 (1974), 207-213. https://doi.org/10.2307/2373587
- H. Omori, Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205-214. https://doi.org/10.2969/jmsj/01920205
- J. Ramanathan, Complete spacelike hypersurfaces of constant mean curvature in de Sitter space, Indiana Univ. Math. J. 36 (1987), no. 2, 349-359. https://doi.org/10.1512/iumj.1987.36.36020
- K. Shiohama and H. Xu, The topological sphere theorem for complete submanifolds, Compositio Math. 107 (1997), no. 2, 221-232. https://doi.org/10.1023/A:1000189116072
- Y. J. Suh, Y. S. Choi, and H. Y. Yang, On space-like hypersurfaces with constant mean curvature in a Lorentz manifold, Houston J. Math. 28 (2002), no. 1, 47-70.
- S. Tanno, A class of Riemannian manifolds satisfying R(X, Y) . R = 0, Nagoya Math. J. 42 (1971), 67-77. http://projecteuclid.org/euclid.nmj/1118798300 https://doi.org/10.1017/S0027763000014240
- M.-J. Wang and Y. Hong, Hypersurfaces with constant mean curvature in a locally symmetric manifold, Soochow J. Math. 33 (2007), no. 1, 1-15.
- H. Xu and X. Ren, Closed hypersurfaces with constant mean curvature in a symmetric manifold, Osaka J. Math. 45 (2008), no. 3, 747-756. http://projecteuclid.org/euclid.ojm/1221656650
- S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228. https://doi.org/10.1002/cpa.3160280203