arXiv subjects

Nicolás Martínez Alba

Publications and source records attributed to Nicolás Martínez Alba.

3 recordsLinked to original sources

arXiv2024

On warped product on information geometry: statistical manifolds and statistical models

We study a differential geometric construction, the warped product, on the background geometry for information theory. Divergences, dual structures and symmetric 3-tensor are studied under this construction, and we show that warped product of manifolds endow with such structure also is endowed with the same geometric notion. However, warped product does not preserve canonical divergences, which in particular shows that warped product lacks of meaning in the information theory setting.

math.DG↗

arXiv2017

Poly-Poisson Sigma models and their relational poly-symplectic groupoids

The main idea of this note is to describe the integration procedure for poly-Poisson structures, that is, to find a poly-symplectic groupoid integrating a poly-Poisson structure, in terms of topological field theories, namely via the path-space construction. This will be given in terms of the poly-Poisson sigma model $(PPSM)$ and we prove that every poly-Poisson structure has a natural integration via relational poly-symplectic groupoids, extending the results in [8] and [26]. We provide familiar examples (trivial, linear, constant and symplectic) within this formulation and we give some applications of this construction regarding the classification of poly-symplectic integrations, as well as Morita equivalence of poly-Poisson manifolds.

math-ph↗

arXiv2017

On the geometry of compatible Poisson and Riemannian structures

We consider compatibility conditions between Poisson and Riemannian structures on smooth manifolds by means of a contravariant partially complex structure, or $f$-structure, introducing the notion of (almost) Kähler--Poisson manifolds. In addition, we study some of their properties under structure preserving maps and symmetries.

math.SG↗