Geometrical Structures of Space-Time in General Relativity (Poster)∗

Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. From the point of view of differential geometry, the space-time is a manifold with a Lorentzian metric. The space-time metric provides different geometrical structures: conformal, volume, projective... A deep understanding of the geometrical structures has consequen-ces on the dynamical role played by geometry. We explain these geo-metrical structures, establishing relationships among them and clari-fying the meaning of associated geometric magnitudes. Recently, some of my research [1,2] have been taken into consid-eration for one of the lines of thought about quantum gravity [3,4]. This poster is a set of my latest reflections and conclusions about the applications of my work to physics. References 1. Sánchez-Rodŕıguez, I., “Intersection of G-structures of first or second or-der”. In O. Kowalski (ed.) et al., Differential geometry and its applications