Acceso abierto

Complete spacelike hypersurfaces with positive r-th mean curvature in a semi-Riemannian warped product


Cite

[1] A. L. Alías, A. Brasil Jr, A. G. Colares, Intergral formulae for space- like hypersurfaces in conformally stationary spacetimes and applications, Proc. Edinb. Math. Soc., 46 (2003), 465-488.10.1017/S0013091502000500Search in Google Scholar

[2] L. J. Alías, A. G. Colares Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker space- times, Math. Proc. Camb. Phil. Soc., 143 (2007), 703-729.10.1017/S0305004107000576Search in Google Scholar

[3] L. J. Alías, M. Dajczer, Uniqueness of constant mean curvature surfaces properly immersed in a slab, Comment. Math. Helv., 81 (2006), 653-663.10.4171/CMH/68Search in Google Scholar

[4] L. J. Alías, D. Impera, M. Rigoli, Hypersurfaces of constant higher order mean curvature in warped profuct spaces, Trans. Amer. Math. Soc., 365 (2013), 591-621.10.1090/S0002-9947-2012-05774-6Search in Google Scholar

[5] L. J. Alías, D. Impera, M. Rigoli, Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson-Walker spacetimes, Math. Proc. Camb. Phil. Soc., 152 (2012), 365-383.10.1017/S0305004111000697Search in Google Scholar

[6] L. J. Alías, A. Romero, M. Sánchez, Uniqueness of complete spacelike hypersurfaces with constant mean curvature in generalized Robertson- Walker spacetimes, Gen. Relat. Grav., 27 (1995), 71-84.10.1007/BF02105675Search in Google Scholar

[7] C. P. Aquino, H. F. de Lima, Uniqueness of complete hypersurfaces with bounded higher order mean curvatures in semi-Riemannian warped products, Glasgow Math. J., 54 (2012), 201-212.10.1017/S0017089511000541Search in Google Scholar

[8] J. L. M. Barbosa, A. G. Colares, Stability of hypersurfaces with constant r-th mean curvature, Ann. Global Anal. Geom., 15 (1997), 277-297.10.1023/A:1006514303828Search in Google Scholar

[9] H. Bondi, T. Gold, On the generation of magnetism by uid motion, Monthly Not. Roy. Astr. Soc., 108 (1948), 252-270.10.1093/mnras/108.3.252Search in Google Scholar

[10] A. Caminha, The geometry of calosed conformal vector fields on Riemannian spaces, Bull. Braz. Math Soc., 42 (2011), 277-300.10.1007/s00574-011-0015-6Search in Google Scholar

[11] A. Caminha, P. Sousa, F. Camargo, Complete foliations of space forms by hypersurfaces, Bull. Braz. Math. Soc., 41 (2010), 339-353.10.1007/s00574-010-0015-ySearch in Google Scholar

[12] F. Camargo, A. Caminha, H. F. de Lima, Bernstein-type theorems in semi-Riemannian warped products, Proc. Amer. Math. Soc., 139 (2011), 1841-1850.10.1090/S0002-9939-2010-10597-XSearch in Google Scholar

[13] A. G. Colares, H. F. de Lima, Some rigidity theorems in semi-Riemannian warped products, Kodai Math. J., 35 (2012), 268-282.10.2996/kmj/1341401051Search in Google Scholar

[14] H. F. de Lima, J. R. de Lima, Complete hypersurfaces immersed in a semi-Riemannian warped product, Differ. Geom. Appl., 30 (2012), 136-143.10.1016/j.difgeo.2011.11.010Search in Google Scholar

[15] F. Hoyle, A new model for the expanding universe, Monthly Not. Roy. Astr. Soc., 108 (1948), 372-382.10.1093/mnras/108.5.372Search in Google Scholar

[16] T. H. Kang, On Lightlike hypersurfaces of a GRW Space-time, Bull. Korean Math. Soc., 49 (2012), 863-874.10.4134/BKMS.2012.49.4.863Search in Google Scholar

[17] S. Montiel, Unicity of constant mean curvature hypersurfaces in some Riemannian manifolds, Indiana Univ. Math. J., 48 (1999), 711-748.10.1512/iumj.1999.48.1562Search in Google Scholar

[18] S. Montiel, Complete non-compact spacelike hypersurfaces of constant mean curvature in de Sitter space, J. Math. Soc. Japan, 55 (2003), 915-938.10.2969/jmsj/1191418756Search in Google Scholar

[19] B. O'Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, New York, 1983.Search in Google Scholar

[20] Y. Wang, X. Liu, On complete spacelike hypersurfaces in a semi- Riemannian warped product, J. Appl. Math., Volume 2013, Article ID 757041, 8 pages10.1155/2013/757041Search in Google Scholar

[21] W. Wang, X. Liu, On Bernstein-type theorems in semi-Riemannian warped products, Adv. Math. Phys., Volume 2013, Article ID 959143, 5 pages10.1155/2013/959143Search in Google Scholar

[22] S. T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J., 25 (1976), 659-670.10.1512/iumj.1976.25.25051Search in Google Scholar

eISSN:
1844-0835
Idioma:
Inglés
Calendario de la edición:
Volume Open
Temas de la revista:
Mathematics, General Mathematics