Developing maps of affinely flat lie groups

Abstract

In this paper, we study the developing maps of the Lie groups with left-invariant affinely flat structures. We make some bacis observations on the nature of the developing images and show that the developing map for an incomplete affine structure splits as a product of a covering map of codimension 1 and a diffeomorphism of dimension 1.

Keywords

• developing map;
• affinely flat;
• left-invariant affinely flat structure;
• left-symmetric algebra

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References

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