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Motivated by the suggestion that Born‐Infeld plasmas could have significance for electron acceleration in neutron star crusts, we obtain an upper bound on the amplitude of electrostatic waves propagating parallel to a longitudinal magnetic field in a Born‐Infeld plasma.
In the present work we consider general relativity coupled to Maxwell’s electromagnetism and charged matter. Under the assumption of spherical symmetry, there is a particular class of solutions that correspond to regular charged black holes whose interior region is de Sitter, the exterior...
We characterize 2‐step nilmanifolds with an abelian complex structure in terms of the existence of a flat connection with parallel torsion.
Natural generalizations of locally symmetric spaces are extended from the Riemannian to the Lorentzian setting and further investigated within the class of Lorentzian Walker manifolds. Explicit examples show that such conditions are meaningless in the higher signature case.
We give a presentation of how one achieves the G 2 ‐twistor space of an oriented Riemannian 4‐manifold M . It consists of a natural SO (3) structure associated to the unit tangent sphere bundle SM of the manifold. Many associated objects permit us to consider also a natural G 2 structure. We...
We provide examples of naturally reductive pseudo‐Riemannian spaces, in particular an example of a naturally reductive pseudo‐Riemannian 2‐step nilpotent Lie group (N,〈,〉 N ), such that 〈,〉 N is invariant under a left action and for which the center is degenerate. The metric does...
We give an overview of the work of Corlette, Donaldson, Hitchin and Simpson leading to the non‐abelian Hodge theory correspondence between representations of the fundamental group of a surface (a surface group ) and the moduli space of Higgs bundles. We then explain how this can be generalized...
I review how geometry enters probability theory, and how it enters quantum mechanics. The logic is similar in both cases, but the latter case is richer and more interesting.
In this note, using previous works of Miatello and Podestá and of the authors, we provide simple, explicit combinatorial conditions for the existence of a spin structure on a diagonal flat manifold. We show in an elementary way that the above conditions are equivalent to the vanishing of the...
In a previous paper the author proved that any flat Legendre foliation on a contact manifold, under certain natural assumptions, admits an Ehresmann connection. In this note we extend such result also to the non‐flat case.