We study the behaviour of the Laplacian flow evolving closed G2-structures on warped products of the form M^6×S^1, where the base M^6 is a compact 6-manifold endowed with an SU(3)-structure. In the general case, we reinterpret the flow as a set of evolution equations on M^6 for the differential forms defining the SU(3)-structure and the warping function. When the latter is constant, we find sufficient conditions for the existence of solutions of the corresponding coupled flow. This provides a method to construct immortal solutions of the Laplacian flow on the product manifolds M^6×S^1. The application of our results to explicit cases allows us to obtain new examples of expanding Laplacian solitons.

Closed warped G2-structures evolving under the Laplacian flow

Anna Fino;Alberto Raffero
2020

Abstract

We study the behaviour of the Laplacian flow evolving closed G2-structures on warped products of the form M^6×S^1, where the base M^6 is a compact 6-manifold endowed with an SU(3)-structure. In the general case, we reinterpret the flow as a set of evolution equations on M^6 for the differential forms defining the SU(3)-structure and the warping function. When the latter is constant, we find sufficient conditions for the existence of solutions of the corresponding coupled flow. This provides a method to construct immortal solutions of the Laplacian flow on the product manifolds M^6×S^1. The application of our results to explicit cases allows us to obtain new examples of expanding Laplacian solitons.
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https://arxiv.org/abs/1708.00222
Anna, Fino; Alberto, Raffero
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1655103
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