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The University of Electro-Communications

Undergraduate: School of Informatics and Engineering, Class I (Informatics), Mathematical Information Engineering Program

Graduate: Graduate School of Informatics and Engineering, Department of Computer and Network Engineering

Marugame Lab

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The lab explores the geometry of CR manifolds using natural metrics.

CR geometryAmbient metricsEinstein metrics

古い数学の報告書 — *Illustrative image. Not taken at the lab.

AboutAbout the lab

Studying CR manifolds through natural metrics

The Marugame Lab studies CR geometry, a branch of geometry.
The lab has studied global invariants of CR manifolds, which appear as boundaries of strictly pseudoconvex domains, using the Cheng-Yau metric on those domains.
The lab has also worked on deepening and refining methods for studying CR manifolds using ambient metrics and complete Einstein metrics.

Key terms

CR manifold: A geometric object that generalizes the structure found on the boundary of a domain in complex space
Metric: A rule for measuring lengths and angles on a geometric object
Conformal geodesic: A natural curve considered in conformal geometry, where only angles matter

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ResearchResearch themes

CR manifolds are geometric objects that appear, for example, as boundaries of domains in complex space. The lab studies invariants and structures of CR manifolds using natural metrics defined on the spaces inside and around them.

*Illustrative image

Ambient Metrics and CR Manifolds

The lab constructed a Hyperkähler ambient metric associated with the twistor CR manifold over a 3-dimensional conformal manifold. It also expressed the Fefferman metric of the twistor CR manifold in a simple form on the original conformal manifold. As an application, it showed that conformal geodesics on a 3-dimensional conformal manifold can be characterized as critical curves of the total torsion functional.

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MembersFaculty

Associate ProfessorTaiji Marugame

VoicesStudent voices

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Research Output

Focus on in-lab researchPublish often at conferences

Topic Freedom

Professor provides topicsChoose your own topic

Supervision

Hands-offClose mentoring

Research Funding

Make do creativelyAmple equipment & funds

Lab Atmosphere

Everyone works quietlyLively and close-knit

Overall Workload

Immersed in researchPlenty of free time

Core hours-

Lab meetings-

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About 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: “Differential geometry of manifolds of figures 1971 cover” 作者不詳 / Public domain (cropped)
Ambient Metrics and CR Manifolds: “Geometry problem-Sb 13088-IMG 0593-white” Rama / CC BY-SA 2.0 fr (cropped)
Related lab (Yamada Lab): “Klein Bottle Parametrized Split Lengthwise” AugPi / CC BY-SA 4.0 (cropped)
Related lab (Tang Lab): “SONYC acoustic sensor nodes deployed in New York City” Charlie Mydlarz; Mohit Sharma; Yitzchak Lockerman; Ben Steers; Claudio Silva; Juan Pablo Bello / CC BY-SA 4.0 (cropped)
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