Translator Disclaimer
March 2020 Surfaces in pseudo-Riemannian space forms with zero mean curvature vector
Naoya Ando
Kodai Math. J. 43(1): 193-219 (March 2020). DOI: 10.2996/kmj/1584345694

Abstract

We characterize a space-like surface in a pseudo-Riemannian space form with zero mean curvature vector, in terms of complex quadratic differentials on the surface as sections of a holomorphic line bundle. In addition, combining them, we have a holomorphic quartic differential. If the ambient space is $S^4$, then this differential is just one given in [5]. If the space is $S^4_1$, then the differential coincides with a holomorphic quartic differential in [6] on a Willmore surface in $S^3$ corresponding to the original surface through the conformal Gauss map. We define the conformal Gauss maps of surfaces in $E^3$ and $H^3$, and space-like surfaces in $S^3_1$, $E^3_1$, $H^3_1$ and the cone of future-directed light-like vectors of $E^4_1$, and have results which are analogous to those for the conformal Gauss map of a surface in $S^3$.

Citation

Download Citation

Naoya Ando. "Surfaces in pseudo-Riemannian space forms with zero mean curvature vector." Kodai Math. J. 43 (1) 193 - 219, March 2020. https://doi.org/10.2996/kmj/1584345694

Information

Published: March 2020
First available in Project Euclid: 16 March 2020

zbMATH: 07196516
MathSciNet: MR4077211
Digital Object Identifier: 10.2996/kmj/1584345694

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

JOURNAL ARTICLE
27 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.43 • No. 1 • March 2020
Back to Top