Riemannian optimisation leverages the geometry of smooth manifolds to reformulate and solve constrained optimisation problems as if they were unconstrained. By utilising techniques such as Riemannian ...

A geodesic in a Riemannian homogeneous manifold (M = G/K, g) is called a homogeneous geodesic if it is an orbit of a one-parameter subgroup of the Lie group G. We investigate G-invariant metrics with ...

Riemannian geometry provides the essential framework for analysing curved spaces by endowing manifolds with a smoothly varying metric. This field has enabled statisticians to extend classical ...

The regularity of optimal routes on sub-Riemannian manifolds has been an important open problem in sub-Riemannian geometry since the early 90s. A researcher now gives new restrictions on the shape of ...

For foliations defined by the orbits of isometric Lie group actions it is shown that the trace of the basic heat kernel admits an asymptotic expansion. The new tehnical aspect in this context is that ...