Identifying Berwald Finsler Geometries

Understand

Berwald geometries are Finsler geometries close to (pseudo)-Riemannian geometries.

• We establish a simple first order partial differential equation as necessary and sufficient condition, which a given Finsler Lagrangian has to satisfy to be of Berwald type.
• Applied to $(\alpha,\beta)$-Finsler spaces, respectively $(A,B)$-Finsler spacetimes, this reduces to a necessary and sufficient condition for the Levi-Civita covariant derivative of the defining $1$-form.
• We illustrate our results with novel examples of $(\alpha,\beta)$-Berwald geometries which represent Finslerian versions of Kundt (constant scalar invariant) spacetimes.