Continued fractions and Einstein manifolds of infinite topological type

Details Continued fractions and Einstein manifolds of infinite topological type Continued fractions and Einstein manifolds of infinite topological type

2005-08-30

arxiv.org/abs/math/0508614v1

Mathematics

Differential Geometry

16 pages; 1 figure

Scientific paper

We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers. These manifolds may be regarded as limits of the resolutions of cyclic quotient singularities (governed by continued fraction expansions of rational numbers) on which we constructed complete self-dual Einstein metrics in previous work.

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