| Project/Area Number |
16H07229
|
|---|
| Research Category |
Grant-in-Aid for Research Activity Start-up
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Tokyo University of Science |
|---|
Principal Investigator |
Yamamoto Hikaru 東京理科大学, 理学部第一部数学科, 助教 (50778173)
|
|---|
| Project Period (FY) |
2016-08-26 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
|---|
| Keywords | mean curvature flow / Lagrangian / special Lagrangian / Ricci flow / mirror symmetry / dHYM connection / 特殊ラグランジュ部分多様体 / 変形エルミート・ヤン・ミルズ接続 / ラグランジュ平均曲率流 / リッチフロー / 平均曲率流 / ラグランジュ部分多様体 |
|---|
| Outline of Final Research Achievements |
I proposed a method to construct a special Lagrange submanifold in the lattice quotient of the tangential bundle of a tropical manifold. I also proved that the Fourier-Mukai transform of this special Lagrange submanifold is a deformed Hermitian Yang Mills connection with support on a complex submanifold in the mirror. A paper on these results will be published in Math. Z.
I proved that if the second fundamental form of a self-shrinker satisfying the pinching condition takes zero at some point, then it becomes a plane. As an application, if a codimension 1 mean curvature flow with initial pinching condition in Euclidean space develops finite time singularities, then all general type I singularities are actually special type I singularities. The proof is summarized in the RIMS Kokyuroku.
|
