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Tanaka Lab
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A differential geometry lab that explores the structure and properties of symmetric spaces.
AboutAbout the lab
Exploring the structure of symmetric spaces through geometry.
The Tanaka Lab studies the structure and properties of symmetric spaces from multiple angles.
Specifically, the lab studies Lie group actions on symmetric spaces, totally geodesic submanifolds, and antipodal sets.
The lab's field is differential geometry, and it also aims to apply its results to other fields.
Key terms
- Symmetric space
- A highly symmetric curved space in which, around every point, there is a symmetric transformation that flips the space about that point
- Lie group
- A group made up of continuously varying transformations, which itself has the form of a smooth space
- Totally geodesic submanifold
- A surface or similar subspace within a space, such that "straight lines" on it are also straight lines in the original space
- Antipodal set
- A set of points in a symmetric space in which every pair of points stands in an exactly opposite relationship to each other
ResearchResearch themes
The Tanaka Lab investigates the structure and properties of symmetric spaces from multiple angles. It also aims to apply its findings to other fields.
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MembersFaculty
- ProfessorMakiko Tanaka
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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: “Poincare Group Commutation Structure” Travisrm89 / CC0 (cropped)
- Structure and Properties of Symmetric Spaces: “Modell einer Minimalfläche mit einer Lemniskate als geodätischer Linie” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Related lab (廣瀬研究室): “Tesseract torus” WatchduckYou can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck". / CC BY 4.0 (cropped)
- Related lab (馬場研究室): “Sarti surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Related lab (江崎研究室): “WienerSausage” R.e.b. / Public domain (cropped)
- Related lab (伊藤・呼子研究室): “Würfel” Dietmar Rabich / CC BY-SA 4.0 (cropped)
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