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 ...

Riemannian geometry provides a foundational framework in which the intrinsic properties of smooth manifolds are studied through the lens of metric structures. At its core, this field is dedicated to ...

Proceedings of the American Mathematical Society, Vol. 138, No. 8 (AUGUST 2010), pp. 2897-2905 (9 pages) We consider the conformal class of the Riemannian product g₀+g, where g₀ is the constant ...

A simply connected solvable Lie group $R$ together with a left-invariant Riemannian metric $g$ is called a (simply connected) Riemannian solv-manifold. Two Riemannian ...

The question of how far geometric properties of a manifold determine its global topology is a classical problem in global differential geometry. Building on recent breakthroughs we investigate this ...

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 ...