The convex cone SC1 SLip(X) of real-valued smooth semi-Lipschitz functions on a Finsler manifold X is an order-algebraic structure that captures both the differentiable and the quasi-metric feature of X. In this work ...

A simple Almost-Riemannian Structure on a Lie group G is defined by a linear vector field (that is an infinitesimal automorphism) and dim(G) - 1 left-invariant ones. It is first proven that two different ARSs are isometric ...

On each solvable Lie group, there is at most one solv- soliton up to isometry and scaling. This allows us to en- dow several Lie groups that do not admit Einstein metrics (e.g., nilpotent or unimodular solvable Lie groups) ...

We study the geodesic orbit property for nilpotent Lie groups N when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When N acts on ...