## Tohoku Mathematical Journal

### Prolongation of holomorphic vector fields on a tube domain

Satoru Shimizu

#### 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.

#### Article information

Source
Tohoku Math. J. (2), Volume 65, Number 4 (2013), 495-514.

Dates
First available in Project Euclid: 6 December 2013

https://projecteuclid.org/euclid.tmj/1386354292

Digital Object Identifier
doi:10.2748/tmj/1386354292

Mathematical Reviews number (MathSciNet)
MR3161430

Zentralblatt MATH identifier
1295.32002

#### Citation

Shimizu, Satoru. Prolongation of holomorphic vector fields on a tube domain. Tohoku Math. J. (2) 65 (2013), no. 4, 495--514. doi:10.2748/tmj/1386354292. https://projecteuclid.org/euclid.tmj/1386354292

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