Tohoku Mathematical Journal

Holomorphic isometric embeddings of the projective line into quadrics

Oscar Macia, Yasuyuki Nagatomo, and Masaro Takahashi

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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.

Article information

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

Dates
First available in Project Euclid: 2 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1512183628

Digital Object Identifier
doi:10.2748/tmj/1512183628

Mathematical Reviews number (MathSciNet)
MR3732886

Zentralblatt MATH identifier
06850812

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.tmj/1512183628


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