Spaces of Riemannian metrics

Snapshots of modern mathematics from Oberwolfach

Spaces of Riemannian metrics

Riemannian metrics endow smooth manifolds such as surfaces with intrinsic geometric properties, for example with curvature. They also allow us to measure quantities like distances, angles and volumes. These are the notions we use to characterize the “shape” of a manifold. The space of Riemannian metrics is a mathematical object that encodes the many possible ways in which we can geometrically deform the shape of a manifold. 

If you are interested in translating this Snapshot, please contact us at

Mathematical subjects

Geometry and Topology


Mauricio Bustamante, Jan-Bernhard Kordaß


DOI (Digital Object Identifier)


Download PDF


snapshots: overview

Mathematical subjects

Algebra and Number Theory
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Humanities and Social Sciences
Life Science
Reflections on Mathematics

These icons are available under the CC BY-SA 4.0 license. Please feel free to use them to classify your own content.
The vector icons can be downloaded here.