Holomorphic isometric embeddings of the projective space into quadrics

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Abstract

We classify holomorphic isometric embeddings of the projective space into quadrics using the generalization of do Carmo–Wallach theory in Nagatomo [Harmonic maps into Grassmann manifolds, arXiv:mathDG/1408.1504[mathDG], Holomorphic maps into Grassmann manifolds (Harmonic maps into Grassmann manifolds III), Annals of Global analysis and Geometry 60, 33–63 (2021). An explicit description of their moduli spaces up to image and gauge equivalence is provided.

Original languageEnglish
Article number31
JournalGeometriae Dedicata
Volume216
Issue number3
DOIs
Publication statusPublished - Jun 2022

Keywords

  • Complex quadric
  • Holomorphic isomorphic embeddings
  • Moduli spaces
  • Projective space
  • Vector bundles

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