| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
The uniqueness problem of linearizations of planar 3-webs under projective transformations is called Gronwall conjecture and still open for more than 100 years. Our research is concerned with Legendrian 3-webs on the 3-dimensional contact space. We proved the uniqueness of linearization map under contact projective transformations for Legendrian d-web when d is greater than 3. This solves the Gronwall conjecture in the (restricted) case above. The proof is given by showing the fundamental theorems, one by one, of contact projective geometry corresponding to those of planar projective geometry.
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