The research of caloric morphism

关于流形之间的热态射，我们得到了如下结果：1。半黎曼流形之间热态射的特征定理，作为黎曼情形的推广.半黎曼流形之间的热态射的时间变量变化和空间伸缩可能依赖于空间变量.半黎曼流形之间的热态射不需要保持时间方向.上述2、3、4的性质表明，热态射的“时间变量变化和空间伸缩与空间变量无关”和“保持时间方向”的性质是拉普拉斯椭圆性的结果。表征热态射的方程与关于加权张力场的热方程相同.将Appell变换推广到半欧几里德空间的情形. 7.同维半欧氏空间之间热态射的判定.径向黎曼度量的穿孔欧氏空间上的热态射的判定.维数大于2.10时径向黎曼度量的穿孔欧氏空间上平移原点的热态射的判定。关于径向半黎曼度量的穿孔欧氏空间上的热态射的判定.关于保多温变换，我们得到了如下结果：保多温变换的特征定理，作为热态射的推广.保多温变换与热态射之间的关系。

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.