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Nagano Lab
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The lab studies the geometry of metric spaces with curvature bounded above.
AboutAbout the lab
Studying the global geometry of metric spaces
The Nagano Lab studies global Riemannian geometry and the geometry of metric spaces.
Its research keywords include Riemannian manifolds, Alexandrov spaces, CAT(k) spaces, and homology manifolds.
The lab investigates the geometric structure of metric spaces with curvature bounded above.
Within the Mathematics Degree Program, the lab belongs to the geometry group.
Key terms
- Riemannian manifold
- A curved space equipped with a way to measure lengths and angles (a Riemannian metric). It is a generalization of curved surfaces to higher dimensions
- CAT(k) space
- A space whose curvature is bounded above by k, defined using only distances. It is a representative example of a metric space with curvature bounded above
- Curvature
- A quantity that expresses how much a space is curved. A sphere has positive curvature, and a flat surface has zero curvature
- Metric space
- A space in which a distance is defined between any two points. It is a framework for treating shapes and surfaces using only distance
ResearchResearch themes
The Nagano Lab studies global Riemannian geometry and the geometry of metric spaces. Focusing on metric spaces with curvature bounded above, it investigates their structure, also drawing on the perspective of geometric topology.
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MembersFaculty
- Associate ProfessorKoichi Nagano
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Lexell's theorem in the hyperbolic plane (half-plane model)” Jacob Rus / CC BY-SA 4.0 (cropped)
- Global Riemannian Geometry of Metric Spaces: “Crochet hyperbolic kelp” Margaret Wertheim / CC BY 2.0 (cropped)
- Related lab (小野 肇 研究室): “Surface of revolution illustration violett” W like wiki / CC BY-SA 4.0 (cropped)
- Related lab (川村 一宏 研究室): “Geometry Lessons” KUHT / Public domain (cropped)
- Related lab (石井 敦 研究室): “Conway knot” Saung Tadashi / CC BY-SA 4.0 (cropped)
- Related lab (丹下 基生 研究室): “Knotted Mobius strip 3” Albert P. Carpenter / CC BY-SA 4.0 (cropped)
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