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Do Barbero-Immirzi connections exist in different dimensions and signatures?

L. Fatibene, Mauro Francaviglia, S. Garruto (2012)

Communications in Mathematics

We shall show that no reductive splitting of the spin group exists in dimension 3 ≤ m ≤ 20 other than in dimension m = 4 . In dimension 4 there are reductive splittings in any signature. Euclidean and Lorentzian signatures are reviewed in particular and signature ( 2 , 2 ) is investigated explicitly in detail. Reductive splittings allow to define a global SU ( 2 ) -connection over spacetime which encodes in an weird way the holonomy of the standard spin connection. The standard Barbero-Immirzi (BI) connection used in LQG is...

Dolbeault homotopy theory and compact nilmanifolds

L. Cordero, M. Fernández, A. Gray, L. Ugarte (1998)

Banach Center Publications

In this paper we study the degeneration of both the cohomology and the cohomotopy Frölicher spectral sequences in a special class of complex manifolds, namely the class of compact nilmanifolds endowed with a nilpotent complex structure. Whereas the cohomotopy spectral sequence is always degenerate for such a manifold, there exist many nilpotent complex structures on compact nilmanifolds for which the classical Frölicher spectral sequence does not collapse even at the second term.

Double linear connections

Alena Vanžurová (1991)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Double vector bundles and duality

Katarzyna Konieczna, Pawel Urbański (1999)

Archivum Mathematicum

The notions of the dual double vector bundle and the dual double vector bundle morphism are defined. Theorems on canonical isomorphisms are formulated and proved. Several examples are given.

Doubly warped product Finsler manifolds with some non-Riemannian curvature properties

Esmaeil Peyghan, Akbar Tayebi, Behzad Najafi (2012)

Annales Polonici Mathematici

We consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas DWP-Finsler manifold is Riemannian. We show that a proper DWP-manifold is Landsbergian if and only if it is Berwaldian. Then we prove that every relatively isotropic Landsberg DWP-manifold is a Landsberg manifold. We show that a relatively isotropic mean Landsberg warped product manifold...

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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