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Ono Lab
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A differential geometry lab exploring the existence of Riemannian metrics on Kähler manifolds and related spaces.
AboutAbout the lab
Searching for canonical metrics on manifolds
The Ono Lab studies differential geometry, particularly Riemannian metrics and the problem of their existence.
It investigates whether canonical metrics exist on spaces with geometric structures, such as Kähler manifolds and Sasaki manifolds.
The lab also works on the research topic "Einstein equations with matter fields and Kähler geometry."
In the Mathematics Degree Program, it belongs to the Geometry Group.
Key terms
- Riemannian metric
- A tool that determines how to measure lengths and angles at each point of a curved space (manifold).
- Kähler manifold
- A space with complex coordinates in which structures such as the Riemannian metric are compatible with one another.
- Sasaki manifold
- An odd-dimensional space with a geometric structure that corresponds to that of a Kähler manifold.
ResearchResearch themes
The lab investigates the existence and properties of Riemannian metrics, centered on the question of whether canonical metrics exist on spaces such as Kähler manifolds and Sasaki manifolds. Its research topics also include Einstein equations with matter fields and Kähler geometry.
*Illustrative imageCanonical Kähler Metrics
The lab studies canonical metrics on Kähler manifolds. A 2024 paper deals with the Einstein-harmonic equations and Kähler metrics of constant scalar curvature.
*Illustrative imageEinstein Equations with Matter Fields
The lab works on research on Einstein equations with matter fields and Kähler geometry.
*Illustrative imageBott Manifolds and the Futaki Invariant
The lab studies Bott manifolds, a type of space, on which the Futaki invariant vanishes for every Kähler class. A 2025 paper is the result of joint research.
MembersFaculty
- ProfessorHajime Ono
VoicesStudent voices
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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: “Surface of revolution illustration violett” W like wiki / CC BY-SA 4.0 (cropped)
- Canonical Kähler Metrics: “CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique ( )” Ecole polytechnique Université Paris-Saclay / CC BY-SA 2.0 (cropped)
- Einstein Equations with Matter Fields: “One-sided spacetime curvatures” Tokamac / CC BY-SA 4.0 (cropped)
- Bott Manifolds and the Futaki Invariant: “Sculpture town park” Danrok / CC BY-SA 3.0 (cropped)
- Related lab (永野 幸一 研究室): “Lexell's theorem in the hyperbolic plane (half-plane model)” Jacob Rus / CC BY-SA 4.0 (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)
- Related lab (川村 一宏 研究室): “Geometry Lessons” KUHT / Public domain (cropped)
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