References
- L. J. Alias, S. C. Garcia-Martinez, and M. Rigoli, A maximum principle for hypersurfaces with constant scalar curvature and applications, Ann. Global Anal. Geom. 41 (2012), no. 3, 307-320. https://doi.org/10.1007/s10455-011-9284-y
- A. Brasil Jr., A. G. Colares, and O. Palmas, Complete hypersurfaces with constant scalar curvature in spheres, Monatsh. Math. 161 (2010), no. 4, 369-380. https://doi.org/10.1007/s00605-009-0128-9
- A. Brasil Jr., A. G. Colares, and O. Palmas, Complete hypersurfaces with constant scalar curvature in spheres, Monatsh. Math. 161 (2010), no. 4, 369-380. https://doi.org/10.1007/s00605-009-0128-9
- E. Cartan, Familles de surfaces isoparametriques dans les espaces a courbure constante, Ann. Mat. Pura Appl. 17 (1938), no. 1, 177-191. https://doi.org/10.1007/BF02410700
-
Q. M. Cheng, Hypersurfaces in a unit sphere
$S^{n+1}$ with constant scalar curvature, J. London Math. Soc. (2) 64 (2001), no. 3, 755-768. https://doi.org/10.1112/S0024610701002587 - Q. M. Cheng and H. Nakagawa, Totally umbilic hypersurfaces, Hiroshima Math. J. 20 (1990), no. 1, 1-10.
- Q. M. Cheng and Susumu, Characterization of the clifford torus, Proc. Amer. Math. Soc. 127 (1999), no. 3, 819-831. https://doi.org/10.1090/S0002-9939-99-05088-1
- S. S. Cheng, M. do Carmo, and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, in Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968), 59-75, Springer, New York, 1970.
- S. Y. Cheng and S. T. Yau, Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), no. 3, 195-204. https://doi.org/10.1007/BF01425237
- S. H. Ding and J. F. Zhang, Hypersurfaces in a locally symmetric manifold with constant mean curvature, Pure Appl. Math. 22 (2006), no. 1, 94-99.
- Z. H. Hou, Hypersurfaces in a sphere with constant mean curvature, Proc. Amer. Math. Soc. 125 (1997), no. 4, 1193-1196. https://doi.org/10.1090/S0002-9939-97-03668-X
- H. B. Lawson, Jr., Local rigidity theorems for minimal hypersurfaces, Ann. of Math. 89 (1969), no. 2, 187-197. https://doi.org/10.2307/1970816
- H. Li, Global rigidity theorems of hypersurfaces, Ark. Mat. 35 (1997), no. 2, 327-351. https://doi.org/10.1007/BF02559973
- H. Li, Y. Suh, and G. Wei, Linear Weingarten hypersurfaces in a unit sphere, Bull. Korean Math. Soc. 46 (2009), no. 2, 321-329. https://doi.org/10.4134/BKMS.2009.46.2.321
- X. X. Liu and H. Li, Complete hypersurfaces with constant scalar curvature in a sphere, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 567-575.
- M. Okumura, Hypersurfaces and a pinching problem on the second fundamental tensor, Amer. J. Math. 96 (1974), no. 4, 207-213. https://doi.org/10.2307/2373587
- S. Pigola, M. Rigoli, and A. G. Setti, Maximum principles on Riemannian manifolds and applications, Mem. Amer. Math. Soc. 174 (2005), no. 822, x+99 pp.
- S. Pigola, A Liouville-type result for quasi-linear elliptic equations on complete Riemannian manifolds, J. Funct. Anal. 219 (2005), no. 2, 400-432. https://doi.org/10.1016/j.jfa.2004.05.009
- B. Segre, Famiglie di ipersuperficie isoparametriche negli spazi euclidei ad un qualunque numero di dimensioni, Atti Accad. Naz. Lincei, Rend., VI. Ser. 27 (1938), 203-207.
- J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math. 88 (1968), no. 2, 62-105. https://doi.org/10.2307/1970556
- S. C. Shu and S. Y. Liu, Complete hypersurfaces with constant mean curvature in locally symmetric manifold, Adv. Math. (China) 33 (2004), no. 5, 563-569.
- H.W. Xu, Pinching theorems, global pinching theorems and eigenvalues for Riemannian submanifolds, Ph. D. dissertation, Fudan University, 1990.
- H.W. Xu, On closed minimal submanifolds in pinched Riemannian manifolds, Trans. Amer. Math. Soc. 347 (1995), no. 5, 1743-1751. https://doi.org/10.1090/S0002-9947-1995-1243175-X
- H. W. Xu and X. Ren, Closed hypersurfaces with constant mean curvature in a symmetric manifold, Osaka J. Math. 45 (2008), no. 3, 747-756.
- S. Zhang and B. Wu, Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces, J. Geom. Phys. 60 (2010), no. 2, 333-340. https://doi.org/10.1016/j.geomphys.2009.10.005
- S. Zhang and B. Wu, Complete hypersurfaces with constant mean curvature in a locally symmetric Riemannian manifold, Acta Math. Sci. Ser. A Chin. Ed. 30 (2010), no. 4, 1000-1005.