Thermonuclear On CR Manifold And Its Asymptotic Expansion

It is very important to study the heat kernel and its asymptotic expansion on manifolds for studying the geometric properties of manifolds,dealing with the index theorem and studying the spectrum of Laplace operator.After introducing the significance of the research topic and the arrangement of the paper,this paper first introduces some basic knowledge of CR manifold and the definition of thermonuclear.The expression of (?)b-Laplace operator ?b on Heisenberg group and CR manifolds acting on external form is calculated respectively,which provides a theoretical basis for the following solution and proof.Then,we construct the heat kernel rt? on the simplest CR manifold Heisenberg group,then we introduce the coordinate system on the CR manifold,and construct the kernel function r by using the hot kernel on Heisenberg group.The Levi algorithm is used for the kernel function r to construct the hot kernel on the CR manifold.A series of properties of the constructed kernel function r are studied,and then the heat kernel on CR manifold is verified and explained in detail.Finally,under the Webster-Stanton connection,the asymptotic expansion of thermonuclear is proved by using the method from special to general,and the first term coefficient K0(x)is obtained.