Born geometry via Künneth structures and recursion operators

Abstract

We propose a simple definition of a Born geometry in the framework of Künneth geometry. While superficially different, this new definition is equivalent to the known definitions in terms of para-quaternionic or generalized geometries. We discuss integrability of Born structures and their associated connections. In particular we find that for integrable Born geometries the Born connection is obtained by a simple averaging under a conjugation from the Künneth connection. We also give examples of integrable Born geometries on nilmanifolds.

29 pages

References in corpus (6)

• Quantum Gravity, Dynamical Phase Space and String Theory
• Generalised Kinematics for Double Field Theory
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• The geometry of recursion operators
• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• Bi-Lagrangian structures on nilmanifolds