2D RICCI FLAT GRADIENT SOLITONS ARISING FROM REMARKABLE MODELS IN PHYSICS

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On a pseudo-Riemannian manifold (M, g) we consider ∇ the Levi-Cività connection associated to metric g and a function f : M → ℝ whose pseudo-Riemannian Hessian [Formula: see text] is non-degenerate and with constant signature. We study properties of the pseudo-Riemannian manifold (M, h), [Formula: see text] in terms of local computation. Investigating the conditions for existence of the equal connections [Formula: see text], produced by g and h, we determine classes of explicit Ricci flat gradient solitons for some particular forms of g, arising from remarkable physics models.