Abstract
A geometric flow on (2, 2)-forms is introduced which preserves the balanced condition of metrics, and whose stationary points satisfy the anomaly equation in Strominger systems. The existence of solutions for a short time is established, using Hamilton’s version of the Nash–Moser implicit function theorem.
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Notes
The usual balanced condition for a Hermitian metric \(\omega \) in dimension n is \(d\omega ^{n-1}=0\). For simplicity, we use the same terminology for the slight modification used in (2.5).
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Work supported in part by the National Science Foundation under Grant DMS-12-66033 and DMS-1308136.
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Phong, D.H., Picard, S. & Zhang, X. Geometric flows and Strominger systems. Math. Z. 288, 101–113 (2018). https://doi.org/10.1007/s00209-017-1879-y
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DOI: https://doi.org/10.1007/s00209-017-1879-y