| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
I studied curves and surfaces with singularities by using moving frames. We gave the definition of evolutes and involutes of frontals in the Eucledian plane. Then we gave relations between geometric properties and singularities of frontals. Moreover, we gave a characterization of convexity of simple closed frontals in the Euclidean plane by using the curvature of the frontal. On surfaces with singularities, as a new approach to study surface with singularities, we introduced a notion of framed surfaces and constructed a fundamental theory. Especially, we defined the fundamental matrices and curvatures of framed surfaces. Then we study on a relation between a properties of the curvatures and a type of singularities.
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