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Differential geometry of grassmannians and the Plücker map

Sasha Anan’in, Carlos Grossi (2012)

Open Mathematics

Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.

Duality of Hodge numbers of compact complex nilmanifolds

Takumi Yamada (2015)

Complex Manifolds

A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.

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