The research of caloric morphism

关于流形间的热态射，我们得到了以下结果：半黎曼流形间热态射的表征定理，作为黎曼情形的推广。半黎曼流形间热态射的时变量变化和空间膨胀可能取决于空间变量。半黎曼流形之间的热态射不需要保留时间方向。上述2、3、4暗示热态射的“时间变量变化的独立性和空间膨胀与空间变量的独立性”和“时间方向的保存性”是拉普拉斯算子椭圆性的结果。描述热态射的方程与关于加权张力场的热方程是相同的。半欧几里得空间中阿佩尔变换的推广。同维半欧几里得空间间热态射的测定。径向黎曼度规刺穿欧几里得空间上热态射的测定。在尺寸大于2.10的情况下，径向黎曼度规在刺穿欧几里得空间上转译原点的热态射的测定。径向半黎曼度规刺穿欧几里得空间上热态射的测定。关于保变换多温度，我们得到了以下结果：作为热模论的推广，得到了保变换多温度的表征定理。保变换多态温度与热态的关系。

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.