Totally real minimal immersions of 𝑛-dimensional real space forms into 𝑛-dimensional complex space forms

Ejiri, Norio

doi:10.1090/S0002-9939-1982-0637177-8

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Totally real minimal immersions of $n$-dimensional real space forms into $n$-dimensional complex space forms
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by Norio Ejiri

Proc. Amer. Math. Soc. 84 (1982), 243-246

DOI: https://doi.org/10.1090/S0002-9939-1982-0637177-8

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Abstract:

$n$-dimensional totally real minimal submanifolds of constant sectional curvature in $n$-dimensional complex space forms are totally geodesic or flat.

References

Bang-yen Chen and Koichi Ogiue, On totally real submanifolds, Trans. Amer. Math. Soc. 193 (1974), 257–266. MR 346708, DOI 10.1090/S0002-9947-1974-0346708-7
Shing Tung Yau, Submanifolds with constant mean curvature. I, II, Amer. J. Math. 96 (1974), 346–366; ibid. 97 (1975), 76–100. MR 370443, DOI 10.2307/2373638