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Honda Lab
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A complex geometry lab that studies the structure of complex manifolds called twistor spaces.
AboutAbout the lab
A slightly unconventional kind of complex manifold.
The Honda Lab studies the structure of three-dimensional complex manifolds known as twistor spaces.
Twistor spaces are somewhat unusual complex manifolds that arise from differential geometry on four-dimensional manifolds.
Building on classical methods based on linear systems, the lab investigates their detailed structure.
For students aiming at the doctoral program, the lab hopes that they will find their own research topics as far as possible, based on what they learn in the lab seminar.
Key terms
- Complex manifold
- A smoothly connected shape or space in which complex numbers can be used as coordinates
- Twistor space
- A three-dimensional complex manifold constructed from the differential-geometric structure of a four-dimensional manifold
- Differential geometry
- A field of mathematics that uses calculus to study how curves, surfaces, and spaces bend
ResearchResearch themes
The lab studies the algebro-geometric structure of three-dimensional complex manifolds called twistor spaces. It deals with complex manifolds arising from the differential geometry of four-dimensional manifolds, which differ somewhat from projective algebraic varieties and compact Kähler manifolds, the mainstream of the field.
*Illustrative imageAlgebraic Geometry of Twistor Spaces
The lab investigates in detail the structure of twistor spaces arising from the differential geometry of four-dimensional manifolds, using classical methods based on linear systems with added refinements.
*Illustrative imageGeometry of Mini-Twistor Spaces
Recently, the lab has been advancing research on the differential-geometric properties of Einstein–Weyl spaces arising from mini-twistor spaces.
MembersFaculty
- ProfessorNobuhiro HondaPublications ↗
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: “Calabi yau” Jbourjai / Public domain (cropped)
- Algebraic Geometry of Twistor Spaces: “Hopf Fibration” Niles Johnson / CC BY 4.0 (cropped)
- Geometry of Mini-Twistor Spaces: “K3 surface” BTotaro / CC BY-SA 4.0 (cropped)
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