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We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures. [ABSTRACT FROM AUTHOR]

The Gauss map of a projective variety X ⊂ PN is a rational map from X to a Grassmann variety. In positive characteristic, we show the following results. (1) For given projective varieties F and Y, we construct a projective variety X whose Gauss map has F as its general fiber and has Y as its image. More generally, we give such construction for families of varieties over Y instead of fixed F. (2) At least in the case when the characteristic is not equal to 2, any inseparable field extension appears as the extension induced from the Gauss map of some X. [ABSTRACT FROM AUTHOR]

Let G be a connected complex Lie group or a connected amenable Lie group. We show that any flat principal G-bundle over any finite CW-complex pulls back to a trivial G-bundle over some finite covering space of the base space if and only if the derived group of the radical of G is simply connected. In particular, if G is a connected compact Lie group or a connected complex reductive Lie group, then any flat principal G-bundle over any finite CW-complex pulls back to a trivial G-bundle over some finite covering space of the base space. [ABSTRACT FROM AUTHOR]