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Title:
Linear stability and integrability of generalized Ricci solitons
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Abstract:
The generalized Ricci solitons are basic objects when we study the stationary points of the generalized Ricci flow. In this lecture, we would like to study the local behavior of the generalized Ricci solitons. First, we compute the second variation of the generalized Einstein-Hilbert functional and deduce that any Bismut flat, compact manifold is linearly stable. Secondly, we study the kernel of the second variation, in other words, they are called infinitesimal deformation. We show some properties of the infinitesimal deformation. In the last part, we focus on the 3-dimensional case and prove that not all infinitesimal deformations are integrable in a 3-dimensional case.
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