| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
For deepening singularity theory, I obtained criteria for Morin singularities for the case of the dimension of the source space and the target space is not the same. By using criteria for Morin singularities, I gave the number of right-left isotopy classes.
For low dimensional geometry, I generalized a formula for the number of singular points and the Euler characteristic to singularities of bundle homomorphisms. I also gave a normal form by only using isometric coordinate transformation of the target space for cuspidal edges and swallowtails. Moreover, I clarified the differential geometric meanings for modulus appeared in the lower degree terms. By using that form, I obtained generic configurations of asymptotic lines and characteristic lines of that singularities. I also studied singularities of solution surfaces of certain differential equation and that of surfaces which approximate the cuspidal edge.
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