Self-dual gravitational instantons and geometric flows of all Bianchi types
Abstract
We investigate four-dimensional, self-dual gravitational instantons endowed with a product structure RxM3, where M3 is homogeneous of Bianchi type. We analyze the general conditions under which Euclidean-time evolution in the gravitational instanton can be identified with a geometric flow of a metric on M3. This includes both unimodular and non-unimodular groups, and the corresponding geometric flow is a general Ricci plus Yang-Mills flow accompanied by a diffeomorphism.
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