Non-existence of flat paracontact metric structures in dimension greater than or equal to five

TL;DR

This paper proves that flat paracontact metric manifolds cannot exist in dimensions five or higher, despite providing a specific example in three dimensions.

Contribution

It demonstrates the non-existence of flat paracontact metric structures in all odd dimensions greater than or equal to five, extending understanding of their geometric properties.

Findings

Constructed a three-dimensional flat paracontact metric manifold

Proved non-existence of such manifolds in dimensions ≥5

Clarified limitations on flat paracontact structures

Abstract

An example of a three dimensional flat paracontact metric manifold with respect to Levi-Civita connection is constructed. It is shown that no such manifold exists for odd dimensions greater than or equal to five.