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Flat slant surfaces in complex projective and complex hyperbolic planes

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Abstract

For surfaces in complex space forms with almost complex structure J, flat surfaces are the simplest ones from intrinsic point of view. From J-action point of view, the most natural surfaces are slant surfaces. The classification of flat slant surfaces in C2 was done in [2]. In this paper we apply a result of [5] to study flat slant surfaces in CP 2 and CH 2. We prove that, for any θ, there exist infinitely many flat θ-slant surfaces in CP 2 and CH 2. And there does not exist flat half-minimal proper slant surface in CP 2 and in CH 2.

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References

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824-1027, USA

    Bang-Yen Chen

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  1. Bang-Yen Chen
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Correspondence to Bang-Yen Chen.

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Chen, BY. Flat slant surfaces in complex projective and complex hyperbolic planes. Results. Math. 44, 54–73 (2003). https://doi.org/10.1007/BF03322913

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  • DOI: https://doi.org/10.1007/BF03322913

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