1999 Fiscal Year Final Research Report Summary
Variation of Singular spaces
| Project/Area Number |
09640086
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | FUKUSHIMA UNIVERSITY |
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Principal Investigator |
MATSUI Akinori Education, Fukushima Univ., Professor, 教育学部, 教授 (70106102)
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| Co-Investigator(Kenkyū-buntansha) |
MAKINO Ryouhei Education, Fukushima Univ., Professor, 教育学部, 教授 (60106953)
ISHII Hiroyuki Education, Fukushima Univ., Professor, 教育学部, 教授 (90007360)
ISU Minoru Education, Fukushima Univ., Professor, 教育学部, 教授 (20007347)
OHASHI Katsuhiro Economic, Fukushima Univ., Professor, 経済学部, 教授 (40007430)
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| Project Period (FY) |
1997 – 1999
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| Keywords | graph / Jacobi field / Hamilton graph / eigenvalue / Walsh series |
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| Research Abstract |
First Matsui studied the variation of a graph embedded in a Riemannian manifold. Let each edge of a graph have the property of springs on tension. Suppose that a graph is embedded in a Riemannian manifold such that each edge is geodesical. On this situation, we will introduce the notion of a tension vector at each vertex of a graph and that of a tension Jacobi field on a graph. If an expanded graph moves in the Euclidian space by the influence of tension, then it moves to such direction that the sum of the sizes of its tension vectors. Then we propose the following.
The sum of the sizes of tension vectors decreases if the graph moves along to the tension Jacobi field. If the ambient Riemannian manifold has negative curvature, this claim is true, but this claim is not always true. We construct examples which are not satisfied with this claim.
Next Matsui studied the generalization of the notion of Hamiltonian graphs. Ishii studied the eigenvalue problem for the system of second order linear differential equations. Ohashi studied the functional central limit theorem for Walsh series with general gaps.
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