| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Research Abstract |
We have succeeded in classifying all of the curvature adopted complete real hyper surfaces in the hyperbolic spaces with constant holomorphic sectional curvature.
It should be emphasized that the constancy of the principal curvatures is not assumed but a consequence. The back ground of the investigation is the critical point theory of distance functions. Our idea applies to the study of the Rauch conjecture on the cut loci and conjugate loci of complete manifolds and of the Alexandrov-Toponogov comparison theorem under the radial curvature assumption.
As a consequence, we have obtained new types of topological sphere theorems under various model surfaces. These results will be useful for the study of convexity on inner metric spaces. Thus, the global study of Riemannian-Finsler Geometry will be seen.
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