| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Outline of Final Research Achievements |
We proved that a parallel mean curvature surface in the non-flat complex space form of complex two dimension, in general, depends on one harmonic function and five real constants. It is the point for the proof to use the Kaehler angle function as one of the coordinates of the surface. In fact, the first and second fundamental forms of the surface can be written in terms of the Kaehler angle function. Moreover, it is proved that the Kaehler angle function is given as an integral transformation of a harmonic function on the surface. Applying these results to the case that the surface is homeomorphic to a torus, we proved that the immersion must be totally real, and hence we determined those tori explicitly.
|
