| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
In an intrinsic metric space, a locally minimizing curve is called a geodesic. We say that a metric space is a geodesic space if any two points can be joined by a minimizing geodesic. H. Busemann put forward the geometry of geodesics in 1955 to study some properties of geodesics, the topological and metric structure of spaces. Using his methods, we produced results on the studies of sets of poles in a Riemannian manifold, the geodesic flows on surfaces and the plane convex billiard ball problems, the Steiner ratio problem for surfaces, a generalization of Toponogov's comparison theorem and some sphere theorems, the relation of a Voronoi diagram and the cut locus. We have a prospect to develop the geometry of geodesics in a non-symmetric intrinsic distance space.
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