The research of caloric morphism

热量态射的研究

基本信息

批准号：
13640151
负责人：
SHIMOMURA Katsunori
金额：
$ 1.66万
依托单位：
IBARAKI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640151/
关键词：
caloric morphism Appell transformation heat equation 熱方程式多重熱作用素の解

项目摘要

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.

关于流形之间的热量形态，我们获得了以下结果：1。半摩曼流形歧管之间热量形态的表征定理，作为雷曼尼亚病例的概括。2。时间变化和空间扩张可能取决于半摩恩良好流形之间的热量形态的空间变量。3。时间方向不必保留半河流流形之间的热量形态。4。高于2、3和4的属性“时间变化的独立性以及空间变量的空间扩张”和“时间方向的保存”和卡路里态态的时间方向是Laplacian椭圆形的结果。5。与加权张力场相对于热量方程的表征的方程与热方程相同。6。将上诉转换扩展到半欧亚岛空间的情况7。同一维度的半欧亚园空间之间的热量形态的测定8。在径向riemannian度量标准的刺穿欧几里得空间上的热量形态的确定。9。在径向riemannian指标的刺穿欧几里得空间上的来源在尺寸大于2.10的情况下的确定，这将radial riemannian度量的欧几里得空间上的起源转化为原来。对径向半河流度量的欧几里得空间的热量形态的确定。在保存多元体的转化中，我们获得了以下结果：作为热量杂种的普遍化，保留多个多元体性的转换定理的表征定理。保存多温体和热量形态的转化之间的关系。