| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
Harmonic map is a critical point of the energy and biharmonic map is the one of the 2-energy. Both theories have been developed greatly in the world. We have clarified the similarities and differences between these theories, recently. We have constructed several examples of biharmonic maps which are not harmonic maps. We gave and clarified the conditions which biharmonic maps must be harmonic maps.
We have constructed and classified all homogeneous biharmonic submanifolds in the symmetric space which are not harmonic.
We gave the similar notions of biharmonic foliations and also pseudo biharmonic submanifolds in Cauchy-Riemannian geometry, and gave several such examples.
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