S^1 \times S^2 as a bag membrane and its Einstein-Weyl geometry

TL;DR

This paper explores the mathematical and geometric properties of an S^1 imes S^2 membrane in the context of hybrid skyrmions, linking topology, general relativity, and hadronic physics.

Contribution

It provides a detailed analysis of the S^1 imes S^2 membrane as a Weyl-Einstein space, connecting differential geometry with hadronic membrane models.

Findings

The S^1 imes S^2 membrane is a Weyl-Einstein space.

Mathematical insights into the topology of the membrane are developed.

Potential applications to hadronic physics and membrane models are discussed.

Abstract

In the hybrid skyrmion in which an Anti-de Sitter bag is imbedded into the skyrmion configuration a S^{1}\times S^{2} membrane is lying on the compactified spatial infinity of the bag [H. Rosu, Nuovo Cimento B 108, 313 (1993)]. The connection between the quark degrees of freedom and the mesonic ones is made through the membrane, in a way that should still be clarified from the standpoint of general relativity and topology. The S^1 \times S^2 membrane as a 3-dimensional manifold is at the same time a Weyl-Einstein space. We make here an excursion through the mathematical body of knowledge in the differential geometry and topology of these spaces which is expected to be useful for hadronic membranes