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Geometria Diferencial

Harmonic energy and geometric non-formality
Dmitri Scheglov

Terça-feira, 5 de junho de 2018, 15:30
Sala 236.

For compact oriented 2n-dimensional manifolds we introduce a "geometric formality" functional on the space of Riemannian metrics which measures the failure of the product of two harmonic n-forms to be harmonic.

For the "first nontrivial case", which is a genus two surface, we were able to completely describe the (essentially) finite-dimensional minimal locus of this functional in the space of all riemannian metrics. All the metrics in the minimal locus have interesting property that their curvature is non-positive and is zero exactly at Weierstrass points.