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Remarks on Special Symplectic Connections

Martin Panák;  Vojtěch Žádník — 2008

Archivum Mathematicum

The notion of special symplectic connections is closely related to parabolic contact geometries due to the work of M. Cahen and L. Schwachhöfer. We remind their characterization and reinterpret the result in terms of generalized Weyl connections. The aim of this paper is to provide an alternative and more explicit construction of special symplectic connections of three types from the list. This is done by pulling back an ambient linear connection from the total space of a natural scale bundle over...

Remarks on Grassmannian Symmetric Spaces

Lenka Zalabová;  Vojtěch Žádník — 2008

Archivum Mathematicum

The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for | 1 | -graded parabolic geometries and for almost Grassmannian structures, in particular. As an application of two general constructions with parabolic geometries, we present an example of non-flat Grassmannian symmetric space. Next we observe there is a distinguished torsion-free...

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