Generalised Potential Functions in Differential Geometry and Information Geometry

Abstract

Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving the inverse problem and also from an intrinsic point of view.

16 pages

References in corpus (6)

• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
• Geometry of quantum systems: density states and entanglement
• Metric on the space of quantum states from relative entropy. Tomographic reconstruction
• A Pedagogical Intrinsic Approach to Relative Entropies as Potential Functions of Quantum Metrics: the $q$-$z$ Family
• Dynamical Vector Fields on the Manifold of Quantum States
• Hamilton-Jacobi Theory and Information Geometry

Cited by in corpus (4)

• Lie groupoids in information geometry
• Einstein's equations and the pseudo-entropy of pseudo-Riemannian information manifolds
• Lifting statistical structures
• Local normal forms of em-wavefronts in affine flat coordinates