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The lagrange intersections for (ℂP n, ℝP n)

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Summary

If (M, ω) is a compact symplectic manifold andL ⊂M a compact Lagrangian submanifold and if φ is a Hamiltonian diffeomorphism ofM then the V. Arnold conjecture states (possibly under additional conditions) that the number of intersection section points ofL and φ (L) can be estimated by #{Lϒφ (L)}≥ cuplength +1. We shall prove this conjecture for the special case (L, M)=(ℝP n, ℂP n) with the standard symplectic structure.

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Authors and Affiliations

  1. Institute of Mathematics, Peking University, 100871, Beijing, China

    Kung-Ching Chang & Mei Yue Jiang

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  1. Kung-Ching Chang
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  2. Mei Yue Jiang
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Chang, KC., Jiang, M.Y. The lagrange intersections for (ℂP n, ℝP n). Manuscripta Math 68, 89–100 (1990). https://doi.org/10.1007/BF02568753

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  • DOI: https://doi.org/10.1007/BF02568753

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