HOLOMORPHIC ISOMETRIC EMBEDDINGS OF THE PROJECTIVE LINE INTO QUADRICS

Oscar Macia; Yasuyuki Nagatomo; Masaro Takahashi

doi:10.2748/tmj/1512183628

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

HOLOMORPHIC ISOMETRIC EMBEDDINGS OF THE PROJECTIVE LINE INTO QUADRICS

Oscar Macia, Yasuyuki Nagatomo, Masaro Takahashi

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Keywords: Holomorphic embeddings, projective line, complex quadric, vector bundles, Einstein–Hermitian connection

JOURNAL FREE ACCESS

2017 Volume 69 Issue 4 Pages 525-545

DOI https://doi.org/10.2748/tmj/1512183628

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Abstract

We discuss holomorphic isometric embeddings of the projective line into quadrics using the generalisation of the theorem of do Carmo–Wallach in [14] to provide a description of their moduli spaces up to image and gauge equivalence. Moreover, we show rigidity of the real standard map from the projective line into quadrics.

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