| 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)
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| 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.
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