A NEW EQUIAFFINE THEORY FOR SURFACES IN ℝ4-Reference-Cited by-同舟云学术

A NEW EQUIAFFINE THEORY FOR SURFACES IN ℝ4

Published:1993-02 Issue:01 Volume:04 Page:127-165
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

NOMIZU KATSUMI¹,VRANCKEN LUC²

Affiliation:

1. Brown University, Department of Mathematics, Providence, RI 02912, USA

2. Katholieke Universiteit Leuven, Department Wiskunde, Celestijnenlaan 200 B, B-3001 Leuven, Belgium

Abstract

In this paper, we investigate the geometry of nondegenerate affine surfaces in ℝ4. The main idea is to introduce an equiaffine structure on the surface by constructing a canonical transversal plane field with the aid of the affine metric. As an application, we then investigate surfaces with vanishing cubic forms. If the affine metric is positive-definite, such a surface can be locally described as a complex curve in [Formula: see text]. On the other hand, if the affine metric is indefinite, such a surface can be seen as the product of two planar curves.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X9300008X

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