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On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles

Takuro Mochizuki (2009)

Annales de l’institut Fourier

In this short survey, we would like to overview the recent development of the study on Deligne-Malgrange lattices and resolution of turning points for algebraic meromorphic flat bundles. We also explain their relation with wild harmonic bundles. The author hopes that it would be helpful for access to his work on wild harmonic bundles.

On Deszcz symmetries of Wintgen ideal submanifolds

Miroslava Petrović-Torgašev, Leopold C. A. Verstraelen (2008)

Archivum Mathematicum

It was conjectured in [26] that, for all submanifolds M n of all real space forms M ˜ n + m ( c ) , the Wintgen inequality ρ H 2 - ρ + c is valid at all points of M , whereby ρ is the normalised scalar curvature of the Riemannian manifold M and H 2 , respectively ρ , are the squared mean curvature and the normalised scalar normal curvature of the submanifold M in the ambient space M ˜ , and this conjecture was shown there to be true whenever codimension m = 2 . For a given Riemannian manifold M , this inequality can be interpreted as follows:...

On F-algebroids and Dubrovin’s duality

John Alexander Cruz Morales, Alexander Torres-Gomez (2019)

Archivum Mathematicum

In this note we introduce the concept of F-algebroid, and give its elementary properties and some examples. We provide a description of the almost duality for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of two anchor maps of a unique cotangent F-algebroid.

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