The Study of caloric morphism

本研究的目的是研究热态射（保持热方程解的变换），重点是显式确定态射。在项目期间，我们获得了以下结果：我们已经确定了常曲率空间的热态射。我们确定了具有不同径向度量的两个半欧几里得空间之间的所有热态射。在此背景下，我们发现了一种新的热态映射，它的空间映射是相似和反转的混合。我们列出了具有不同径向度量的两个半欧几里得空间之间的基本热态射。我们把所有的热态射表示为基本热态射的组合。

The purpose of this research is the study of the caloric morphism (the transformation which preserve the solution of the heat equation), focusing on the explicit determination of the morphism.We obtained the following results in the term of the project.1. We have determined the caloric morphism for constant curvature spaces.2. We determined all the caloric morphism between two semi-euclidean spaces with different radial metrics. As a result, we found a new type of caloric morphism in this setting, whose space mapping is the mixture of the similarity and the inversion.3. We made the list of fundamental caloric morphisms between two semi-euclidean spaces with different radial metrics. And we gave a representation of all the caloric morphism as a composition of the fundamental caloric morphisms.