Study on identites for generalized gradients associated to geometric structures and their applications
Project/Area Number |
15K04858
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Waseda University |
Principal Investigator |
HOMMA Yasushi 早稲田大学, 理工学術院, 教授 (50329108)
|
Project Period (FY) |
2015-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
Keywords | スピン幾何学 / ラリタ-シュインガー作用素 / ディラック作用素 / ワイゼンベック公式 / 幾何構造 / ラプラス作用素 / アインシュタイン多様体 / 対称空間 |
Outline of Final Research Achievements |
The purpose of this project is to find new identities for generalized gradients related to geometric structures and apply them to geometry, harmonic analysis and theoretical physics.Here,a generalized gradient is a conformally covariant 1st differential operator on a spin manifold such as the Dirac operator and the Rarita-Schwinger operator. Doing an international joint research, we have the following results: (1) We give the twisted Weitzenb\"ock formula explicitly which is a unique relation for generalized gradients on two different vector bundles. We also give some applications such as a commutative relation for Lichnerowicz Laplacian and a generalized gradient. (2) We clarify a relation between Rarita-Schwinger fields and some geometric structures. We also give a classification of spin manifolds admitting parallel 3/2-spin fields.
|
Report
(4 results)
Research Products
(10 results)