| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
As singularity theory of differential geometry and its applications, we have studied a theory of Legendre curves, framed cuvres and framed surfaces. We gave the existence and the uniqueness for them by using the curvatures or the basic invariants. We investigated the evolutes, involutes, envelopes and focal surfaces for Legendre curves and framed curves. Moreover, we gave a generic classification of bifurcations of Lagrangian submanifold germs by one-parameter Lagrangian equivalence. Furthermore, we gave a generic classifications of tangent surfaces associated with Dn geometry and studied the properties from the viewpoint of differential geometry and differential equations.
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