10 citations · 11 across the 6 of their papers we have counts for
6 papers
Metric tensors and two-forms in information geometry from the GNS construction
Marco Castrillón López, Florio M. Ciaglia, Laura González-Bravo +1
We develop a GNS-based construction of geometric tensors on smooth parametric statistical models over -algebras. Since the state space of a -algebra is generally not a sm…
The Ambrose-Singer Theorem for general homogeneous manifolds with applications to symplectic geometry
J. L. Carmona Jimenez, M. Castrillon Lopez
The main result of this article provides a characterization of reductive homogeneous spaces equipped with some geometric structure (non necessarily pseudo-Riemannian) in terms of t…
The Equivalence Problem of Curves in a Riemannian Manifold
M. Castrillon Lopez, V. Fernandez Mateos, J. Munoz Masque
The equivalence problem of curves with values in a Riemannian manifold, is solved. The domain of validity of Frenet's theorem is shown to be the spaces of constant curvature. For a…
Reduction of Homogeneous Riemannian Structures
M. Castrillon Lopez, I. Lujan
The goal of this article is the study of homogeneous Riemannian structure tensors within the framework of reduction under a group of isometries. In a first result, is a nor…
The canonical 8-form on manifolds with holonomy group Spin(9)
M. Castrillon Lopez, P. M. Gadea, I. Mykytyuk
An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of e…
Homogeneous quaternionic Kaehler structures and quaternionic hyperbolic space
M. Castrillon Lopez, P. M. Gadea, A. F. Swann
An explicit classification of homogeneous quaternionic Kaehler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. W…