Tokyo Journal of Mathematics

On a Variety of Algebraic Minimal Surfaces in Euclidean 4-Space

Katsuhiro MORIYA

Full-text: Open access

Abstract

In this paper, we show that the moduli space of the Weierstrass data for algebraic minimal surfaces in Euclidean 4-space with fixed topological type, orders of branched points and ends, and total curvature, has the structure of a real analytic variety. We provide the lower bounds of its dimension. We also show that the moduli space of the Weierstrass data for stable algebraic minimal surfaces in Euclidean 4-space has the structure of a complex analytic variety.

Article information

Source
Tokyo J. Math., Volume 21, Number 1 (1998), 121-134.

Dates
First available in Project Euclid: 31 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1270041990

Digital Object Identifier
doi:10.3836/tjm/1270041990

Mathematical Reviews number (MathSciNet)
MR1630151

Zentralblatt MATH identifier
0958.53008

Citation

MORIYA, Katsuhiro. On a Variety of Algebraic Minimal Surfaces in Euclidean 4-Space. Tokyo J. Math. 21 (1998), no. 1, 121--134. doi:10.3836/tjm/1270041990. https://projecteuclid.org/euclid.tjm/1270041990


Export citation