2002 Fiscal Year Final Research Report Summary
The research of caloric morphism
| Project/Area Number |
13640151
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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 |
Basic analysis
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| Research Institution | IBARAKI UNIVERSITY |
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Principal Investigator |
SHIMOMURA Katsunori IBARAKI Univ., college of Science, Associate Professor, 理学部, 助教授 (00201559)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIO Masaharu Osaka City Univ., Graduate School of Science, Associate professor, 大学院・理学研究科, 助教授 (90228156)
SUZUKI Noriaki Nagoya Univ., Graduate School of Mathematics, Associate professor, 大学院・多元数理科学研究科, 助教授 (50154563)
HORIUCHI Toshio IBARAKI Univ., college of Science, Professor, 理学部, 教授 (80157057)
ANDO Hiroshi IBARAKI Univ. college of Science, Research Associate, 理学部, 助手 (60292471)
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| Project Period (FY) |
2001 – 2002
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| Keywords | caloric morphism / Appell transformation / heat equation / 熱方程式 |
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| Research Abstract |
On caloric morphisms between manifolds, we obtained the following results :
1. The characterization theorem for caloric morphism between semi-riemannian manifolds, as a generalization of the reimannian case.
2. The time variable change and the space dilatation may depend on the space variable for caloric morphisms between semi-riemannian manifolds.
3. The time direction need not be preserved for caloric morphisms between semi-riemannian manifolds.
4. Above 2, 3, and 4 imply that the properties "independence of the time variable change and the space dilatation from the space variable" and "preservation of the time direction" of caloric morphism are the results of the ellipticity of the Laplacian.
5. The equation which characterize the caloric morphism is the same as the heat equation with respect to the weighted tension field.
6. Extension of the Appell transformations to the case of semi-euclidean spaces.
7. The determination of the caloric morphism between semi-euclidean spaces of same dimensions.
8. The determination of the caloric morphism on punctured euclidean space of radial riemannian metric.
9. The determination of the caloric morphism which translates the origin on punctured euclidean space of radial riemannian metric in the case that the dimension is greater than 2.
10. The determination of the caloric morphism on punctured euclidean space of radial semi-riemannian metric.
On the transformation preserving poly-temperatures, we obtained the following results :
The characterization theorem for the transformation preserving poly-temperatures, as a generalization of the caloric merphism. The relation between the transformation preserving poly-temperatures and caloric morphisms.
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