Harmonic Ricci Flow on surfaces
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چکیده
Let g(t) be a family of smooth Riemannian metrics on an n-dimensional closed manifold M . Moreover, given a smooth closed Riemannian manifold (N, gN ) of arbitrary dimension, let φ(t) be a family of smooth maps from M to N . Then (g(t), φ(t)) is called a solution of the volume preserving Harmonic Ricci Flow (or Ricci Flow coupled with Harmonic Map Heat Flow), if it satisfies ∂tg = −2 Ricg + 2α dφ⊗ dφ+ 2 n g M ( Rg − α|dφ|g ) dμg =: T (g, φ),
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تاریخ انتشار 2017