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 ...

Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 52 (100), No. 3 (2009), pp. 271-279 (9 pages) In the setting of a closed Riemannian manifold endowed ...

In this paper, we obtain some classification theorems for totally umbilical semi-invariant sub-manifolds in locally decomposable metallic Riemannian manifolds. We also prove that there exist no ...

Eigenvalue problems on Riemannian manifolds lie at the heart of modern geometric analysis, bridging the gap between differential geometry and partial differential equations. In this framework, the ...

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 ...

A classical question in Riemannian geometry is to ask “from what geometric information about the Riemannian manifold can one determine the metric?”. For 2-dimensional, compact, simple manifolds with ...

Current Projects • EXC 2044 - B1: Smooth, singular and rigid spaces in geometry Many interesting classes of Riemannian manifolds are precompact in the Gromov-Hausdorfftopology. The closure of such a ...

Differential manifolds provide higher dimensional generalizations of surfaces. They appear in a very natural manner in many areas of mathematics and physics. On a differential manifold or more ...

The regularity of optimal routes on sub-Riemannian manifolds has been an important open problem in sub-Riemannian geometry since the early 90s. In his thesis, FM Eero Hakavuori gives new restrictions ...