| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
Referring to results of over-determined systems on surfaces in the Euclidean space, I obtained the corresponding results of over-determined systems on surfaces in the other 3-dimensional space forms. I obtained characterizations of spacelike surfaces with zero mean curvature vector in the 4-dimensional Riemannian and Lorentz space forms in terms of the induced metrics and principal distributions w.r.t. suitable normal vector fields. A minimal surface in the 4-dimensional Euclidean space s.t. principal curvatures do not depend on the choice of a unit normal vector is congruent with a complex curve in the two-dimensional complex number space and characterized in terms of the induced metric and a holomorphic cubic differential. In relation to this characterization, any complex curve is locally considered as the image of the composition of an affine Schwarz map and a parallel translation. I obtained a characterization of a sphere Schwarz immersion in terms of a positive-valued function.
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