The Study of caloric morphism

本研究的目的是研究热量态射(保持热方程解的变换)，着重于态射的明确确定。我们确定了常曲率空间的热量态射。我们确定了两个具有不同径向度量的半欧氏空间之间的所有热量态射。结果，我们发现了一种新的热量形态，它的空间映射是相似和反转的混合体。我们列出了两个具有不同径向度量的半欧氏空间之间的基本热量态射。我们给出了所有热量态射的表示，作为基本热量态射的组成。

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.