General relativity, differential geometry, and unitary theories in the work of Mira Fernandes

An analysis of the work of Mira Fernandes on unitary theories is presented.Comment: 3 page

Black holes and fundamental physics

We give a review of classical, thermodynamic and quantum properties of black holes relevant to fundamental physics.Comment: Invited talk at the Fifth International Workshop on New Worlds in Astroparticle Physics, University of the Algarve, Faro, Portugal, January 8-10, 2005, published in the Proceedings of the Fifth International Workshop on New Worlds in Astroparticle Physics, World Scientific (2006), eds. Ana M. Mour\~ao et al., p. 71-9

Cyclic homogeneous Riemannian manifolds

In spin geometry, traceless cyclic homogeneous Riemannian manifolds equipped with a homogeneous spin structure can be viewed as the simplest manifolds after Riemannian symmetric spin spaces. In this paper, we give some characterizations and properties of cyclic and traceless cyclic homogeneous Riemannian manifolds and we obtain the classification of simply-connected cyclic homogeneous Riemannian manifolds of dimension less than or equal to four. We also present a wide list of examples of non-compact irreducible Riemannian $3$-symmetric spaces admitting cyclic metrics and give the expression of these metrics

Homogeneous spin Riemannian manifolds with the simplest Dirac operator

We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds $(M,g)$ which are traceless cyclic with respect to some quotient expression $M=G/K$ and reductive decomposition $\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{m}$. Using transversally symmetric fibrations of noncompact type, we give a list of them