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Keywords:
totally real submanifolds; pinching; totally geodesic
Summary:
In this paper, we obtain some pinching theorems for totally real minimal submanifolds in complex projective space.
References:
[CO] Chen, B. Y. and Ogiue, K.: On totally real submanifolds. Trans. Amer. Math. Soc. 193 (1994), 257–266. MR 0346708
[LC] Li, Y. W and Chao, X. L.: A modified version of Simons formula. preprint (2001), .
[M1] Matsuyama, Y.: Curvature pinching for totally real submanifolds of complex projective space. J. Math. Soc. Japan 52 (2000), 51–64. MR 1727200
[M2] Matsuyama, Y.: On totally real submanifolds of a complex projective space. Nihonkai Math. J. 13 (2002), 153–157. MR 1947932 | Zbl 1041.53036
[MRU] Montiel, S., Ros, A. and Urbano, F.: Curvature pinching and eigenvalue rigidity for minimal submanifolds. Math. Z. 191 (1986), 537-548. MR 0832811
[O] Ogiue, K.: Recent topics of differential geometry. Mathematics: the publication of the Mathematical Society of Japan 39 (1987), 51–64.
[R1] Ros, A.: A characterization of seven compact Kahler submanifolds by holomorphic pinching. Ann. Math. 121 (1985), 377–382. MR 0786353
[R2] Ros A.: Eigenvalue inequalities for minimal submanifolds and P-manifolds. Math. Z. 187 (1984), 393–404. MR 0757479
[R3] Ros, A.: On spectral geometry of Kaehlar submanifolds. J. Math. Soc. Japan 36 (1984), 433–448. MR 0746704
[Si] Simons, J.: Minimal verieties in Riemannian manifolds. Ann. Math. 88 (1968), 62–65. MR 0233295
[Sh1] Shen, Y. B.: Totally real minimal submanifolds in quaternionic projective space. Chin. Ann. Math. 14B (1993), 297–306. MR 1264303
[Sh2] Shen, Y. B.: On scalar curvature of totally real minimal submanifolds. Chin. Ann. Math. 12A (1991), 573–577. MR 1153942
[Sh3] Shen, Y. B.: On curvature pinching for minimal and Kahler submanifolds with isotropic second fundamental form. Chin. Ann. Math. 12B (1991), 454–463. MR 1154632
[Ub] Urbano F.: Totally real submanifolds. Geometry and Topology of Submanifolds, Proceedings (1987), 198–208. MR 1116144
[X] Xia, C. Y.: On the minimal submanifolds in $CP^m(c)$ and $S^n(1)$. Kodai Math. J. 15 (1992), 141–153. MR 1156896
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