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.
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Acknowledgements
The author is grateful to Prof. O. Macia for useful conversations. This research is supported by JSPS KAKENHI Grant Number 17K05230.
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Nagatomo, Y. Holomorphic isometric embeddings of the projective space into quadrics. Geom Dedicata 216, 31 (2022). https://doi.org/10.1007/s10711-022-00689-4
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DOI: https://doi.org/10.1007/s10711-022-00689-4