A heat flow for special metrics

On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in G2. We prove short-time existence and uniqueness for its negative gradient flow. Furthermore, we show that the flow exists for all times and converges m...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 231; no. 6; pp. 3288 - 3322
Main Authors Weiß, Hartmut, Witt, Frederik
Format Journal Article
LanguageEnglish
Published Elsevier Inc 20.12.2012
Subjects
[formula omitted]-manifolds
Geometric evolution equations
Quasilinear parabolic equations
secondary
G2-manifolds
Geometric evolution equations
Quasilinear parabolic equations
primary
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Summary:On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in G2. We prove short-time existence and uniqueness for its negative gradient flow. Furthermore, we show that the flow exists for all times and converges modulo diffeomorphisms to some critical point for any initial condition sufficiently C∞-close to a critical point.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2012.08.007