Tohoku Mathematical Journal
2017
December
SECOND SERIES VOL. 69, NO. 4

Tohoku Math. J.
69 (2017), 525-545

Title HOLOMORPHIC ISOMETRIC EMBEDDINGS OF THE PROJECTIVE LINE INTO QUADRICS

Author Oscar Macia, Yasuyuki Nagatomo and Masaro Takahashi

(Received May 15, 2015, revised November 4, 2015)
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.

Mathematics Subject Classification. Primary 32H02; Secondly 53C07.
Key words and phrases. Holomorphic embeddings, projective line, complex quadric, vector bundles, Einstein--Hermitian connection.

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