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1999 Fiscal Year Final Research Report Summary

Variation of Singular spaces

Research Project

Project/Area Number 09640086
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionFUKUSHIMA UNIVERSITY

Principal Investigator

MATSUI Akinori  Education, Fukushima Univ., Professor, 教育学部, 教授 (70106102)

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)
Project Period (FY) 1997 – 1999
Keywordsgraph / Jacobi field / Hamilton graph / eigenvalue / Walsh series
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.

  • Research Products

    (2 results)

All Other

All Publications (2 results)

  • [Publications] Hiroyuki ISHII: "A generalization of eigenvalue probles for system of second order linear differential equations"Science reports of Fukushima Univ.. 63. 1-11 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Katuhiro OHASHI: "On the functional central limit theorem for Walsh series with general gaps"Shogaku Ronshu. 67. 81-90 (1999)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2001-10-23  

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