Cauchy-Kowalevski's theorem applied for counting geometric structures

TL;DR

This paper uses the Cauchy-Kowalevski theorem to determine the number of geometric structures, such as linear connections and statistical structures, with prescribed Ricci tensors in the analytic setting.

Contribution

It applies the Cauchy-Kowalevski theorem to solve counting problems for geometric structures with specific Ricci tensor conditions.

Findings

Quantifies the number of linear connections with given Ricci tensor.

Determines the count of statistical structures with prescribed Ricci tensor.

Provides an analytic approach to geometric structure classification.

Abstract

How many are linear connections with prescribed Ricci tensor? How many are statistical structures? The questions are answered in the analytic case by using the Cauchy-Kowalewski theorem.