| Budget Amount *help |
¥3,670,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥570,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Research Abstract |
We have studied a qualitative theory for implicit ordinary differential equations and given existence and uniqueness conditions for complete solutions of implicit ordinary differential equations. Moreover, we classified types of completely integrable second order implicit ordinary differential equations. We also have studied differential geometry and given generic classifications of tangent surfaces of Legendre curves and null curves respectively. Furthermore, we gave relationship between caustics of submanifolds and of a canal hypersurface of the submanifolds.
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