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Baba Lab
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The lab explores the geometric structures of symmetric spaces and related objects through differential geometry.
AboutAbout the lab
Exploring the geometric structures of manifolds through differential geometry.
Within differential geometry, the Baba Lab conducts research with a particular interest in symmetric spaces, calibrated geometry, and the geometry of connections.
In geometry and mathematical physics, the objects of study are "manifolds," a concept that generalizes geometric figures.
In the study of manifolds, the holonomy group makes it possible to capture the properties of the geometric structures a manifold has.
In this lab, we clarify the properties of the geometric structures of manifolds known as symmetric spaces and hyperkähler manifolds.
Key terms
- Manifold
- A concept that generalizes geometric figures. It is an object of study in geometry and mathematical physics
- Holonomy group
- Holonomy refers to the twisting that results from parallel transport, and a group is a notion of symmetry. It makes it possible to capture the properties of a manifold's geometric structure
- Symmetric space
- A space whose foundational theory was established by Cartan. Lie group actions on it are also objects of study
- Calibration
- A concept introduced by Harvey and Lawson, originating in the study of minimal submanifolds in Riemannian manifolds
ResearchResearch themes
Within differential geometry, the lab studies symmetric spaces, calibrated geometry, and the geometry of connections. It aims to clarify the properties of the geometric structures of manifolds known as symmetric spaces and hyperkähler manifolds.
*Illustrative imageGeometry of Symmetric Spaces
The main objects of study are symmetric spaces and Lie group actions on them. Building on the foundational theory established by Cartan, the lab aims to address classification problems concerning symmetric spaces and to discover new dualities.
*Illustrative imageCalibrated Geometry
The main objects of study are calibrations and the concept of calibrated submanifolds. These are closely related to geometric structures that are invariant under the holonomy group of a Riemannian manifold, and the lab investigates such objects.
*Illustrative imageGeometry of Connections
In the area concerning connections and curvature, the lab studies Yang-Mills connections and Yang-Mills-type connections, which generalize them. This field also attracts the attention of physicists in the form of gauge theory.
MembersFaculty
- Associate ProfessorKurando Baba
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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: “Sarti surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Geometry of Symmetric Spaces: “EB1911 - Geometry Fig. 9” 作者不詳 / Public domain (cropped)
- Calibrated Geometry: “Horgan's minimal non-surface” Anders Sandberg / CC BY 4.0 (cropped)
- Geometry of Connections: “Z2 principal bundle over circle” Tazerenix / CC BY-SA 4.0 (cropped)
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