Biharmonic maps extend the concept of harmonic maps by exploring critical points of higher order energy functionals. In Riemannian geometry, while harmonic maps minimise the classical energy ...

Eigenvalue problems occupy a central role in Riemannian geometry, providing profound insights into the interplay between geometry and analysis. At their core, these problems involve the study of ...

We consider the multivariate normal model as a differentiable manifold, equipped with the Fisher information as Riemannian metric, and derive the enduced geometry, i.e., the affine connection, the ...

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 ...

Hamilton's Ricci flow is a (weakly parabolic) geometric evolution equation, which deforms a given Riemannian metric in its most natural direction. Over the last decades, it has been used to prove ...

Bernhard Riemann was a man with a hypothesis. He was confident that it was true, probably. But he didn’t prove it. And attempts over the last century and a half by others to prove it have failed. A ...