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Minimal symplectic atlases of Hermitian symmetric spaces

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Abstract

In this paper we estimate the minimal number of Darboux charts needed to cover a Hermitian symmetric space of compact type \(M\) in terms of the degree of their embeddings in \(\mathbb {C}P^N\). The proof is based on the recent work of Rudyak and Schlenk (Commun Contemp Math 9(6):811–855, 2007) and on the symplectic geometry tool developed by the first author in collaboration with Loi et al. (J Sympl Geom, 2014). As application we compute this number for a large class of Hermitian symmetric spaces of compact type.

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Acknowledgments

The authors would like to thank Professor Andrea Loi for his help and various stimulating discussions and Professor Felix Schlenk for his interest in our work and his valuable comments.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli studi di Cagliari, Cagliari, Italy

    Roberto Mossa

  2. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Giovanni Placini

Authors
  1. Roberto Mossa
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  2. Giovanni Placini
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Corresponding author

Correspondence to Roberto Mossa.

Additional information

Communicated by Vicente Cortés.

R. Mossa was supported by Prin 2010/11—Varietà reali e complesse: geometria, topologia e analisi armonica—Italy.

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Mossa, R., Placini, G. Minimal symplectic atlases of Hermitian symmetric spaces. Abh. Math. Semin. Univ. Hambg. 85, 79–85 (2015). https://doi.org/10.1007/s12188-015-0107-0

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  • DOI: https://doi.org/10.1007/s12188-015-0107-0

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