Tohoku Mathematical Journal
2013
December
SECOND SERIES VOL. 65, NO. 4

Tohoku Math. J.
65 (2013), 495-514

Title PROLONGATION OF HOLOMORPHIC VECTOR FIELDS ON A TUBE DOMAIN

Author Satoru Shimizu

(Received May 24, 2012, revised November 27, 2012)
Abstract. In this paper, we discuss some algebraic criterion on the completeness of holomorphic vector fields on a tube domain $T_\Omega$. Our objects of consideration are polynomial vector fields on $T_\Omega$. We give a method of determining the higher degree complete polynomial vector fields from the data on the lower degree complete polynomial vector fields, which we call prolongation. Furthermore, we give its applications to the holomorphic equivalence problem for tube domains.

Mathematics Subject Classification. Primary 32A07; Secondary 32M05.
Key words and phrases. Tube domains, Holomorphic vector fields.

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