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math.DG2025
On three-dimensional Poisson quasi-Nijenhuis manifolds and Haantjes structures
E. Chuño Vizarreta, I. Mencattini, M. Pedroni
In this note we first characterize Poisson quasi-Nijenhuis structures on three-dimensional oriented manifolds whose underlying Poisson tensor never vanishes. We then apply this res…
math.DG2021★ 10 cited
A Dubrovin-Frobenius manifold structure of NLS type on the orbit space of
Alessandro Arsie, Paolo Lorenzoni, Igor Mencattini +1
Generalizing a construction presented in [3], we show that the orbit space of less the image of coordinate lines under the quotient map is equipped with two Dubrovin-Frobeniu…
math.DG2003★ 10 cited
Hyper-symplectic structures on integrable systems
C. Bartocci, I. Mencattini
We prove that an integrable system over a symplectic manifold, whose symplectic form is covariantly constant w.r.t. the Gauss-Manin connection, carries a natural hyper-symplectic s…