Totally real submanifolds with nonnegative sectional curvature
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- by Yoshihiro Ohnita PDF
- Proc. Amer. Math. Soc. 97 (1986), 474-478 Request permission
Abstract:
We prove that an $n$-dimensional compact totally real submanifold immersed in an $n$-dimensional complex space form with parallel mean curvature vector and nonnegative sectional curvature has parallel second fundamental form. Combining our result and Naitoh’s works we obtain the classification of such submanifolds.References
- Bang-Yen Chen and Chorng Shi Houh, Totally real submanifolds of a quaternion projective space, Ann. Mat. Pura Appl. (4) 120 (1979), 185–199. MR 551066, DOI 10.1007/BF02411943
- Bang-yen Chen, Chorng Shi Houh, and Huei Shyong Lue, Totally real submanifolds, J. Differential Geometry 12 (1977), no. 4, 473–480 (1978). MR 512918
- Alfred Gray, Compact Kähler manifolds with nonnegative sectional curvature, Invent. Math. 41 (1977), no. 1, 33–43. MR 474161, DOI 10.1007/BF01390163
- Alfred Gray, Einstein-like manifolds which are not Einstein, Geom. Dedicata 7 (1978), no. 3, 259–280. MR 505561, DOI 10.1007/BF00151525
- Hiroo Naitoh, Parallel submanifolds of complex space forms. I, Nagoya Math. J. 90 (1983), 85–117. MR 702254, DOI 10.1017/S0027763000020365
- Hiroo Naitoh, Parallel submanifolds of complex space forms. I, Nagoya Math. J. 90 (1983), 85–117. MR 702254, DOI 10.1017/S0027763000020365
- Koichi Ogiue, Positively curved totally real minimal submanifolds immersed in a complex projective space, Proc. Amer. Math. Soc. 56 (1976), 264–266. MR 400129, DOI 10.1090/S0002-9939-1976-0400129-4
- Francisco Urbano, Totally real minimal submanifolds of a complex projective space, Proc. Amer. Math. Soc. 93 (1985), no. 2, 332–334. MR 770548, DOI 10.1090/S0002-9939-1985-0770548-0
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 474-478
- MSC: Primary 53C40
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840632-2
- MathSciNet review: 840632