Tohoku Mathematical Journal

Holomorphic isometric embeddings of the projective line into quadrics

Oscar Macia, Yasuyuki Nagatomo, and Masaro Takahashi

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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.

Article information

Tohoku Math. J. (2), Volume 69, Number 4 (2017), 525-545.

First available in Project Euclid: 2 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
Secondary: 53C07: Special connections and metrics on vector bundles (Hermite-Einstein- Yang-Mills) [See also 32Q20]

holomorphic embeddings projective line complex quadric vector bundles Einstein-Hermitian connection


Macia, Oscar; Nagatomo, Yasuyuki; Takahashi, Masaro. Holomorphic isometric embeddings of the projective line into quadrics. Tohoku Math. J. (2) 69 (2017), no. 4, 525--545. doi:10.2748/tmj/1512183628.

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