複流型上的陳里奇流

Abstract

本文主要在研究陳里奇流在具有埃米爾特點積的複流型上，並介紹了一些Tosatti與Weinkove所證明的重要的結果。此外，我們也研討了陳里奇流在一些非凱勒曲面上的行為。第一部分中我們主要介紹了一些陳里奇流的現代結果與我們的結果。第二部分為讀者方便起見，收錄了一些基本的術語合常用的記號。第三至第七部分則介紹了一些Tosatti與Weinkove的定理證明。最後，我們嘗試了在廣義的霍普夫曲面上，使用用特殊的戈迪雄點積調查陳里奇流。

In this master thesis, we study the Chern-Ricci flow on the complex Hermitian manifolds and introduce the results proved by Tosatti and Weinkove. Moreover, we investigate the Chern-Ricci flow on some non-Kähler surfaces. In the first section, we introduce some modern results of the Chern-Ricci flow and our result. In the second part, we include some well-known notation and conventions for reader’s convenience. From the third part to the seventh part, we introduce the proofs of some modern theorems proved by Tosatti and Weinkove. Finally, we investigate the Chern-Ricci flow starting with a special Gauduchon metric on the general Hopf surfaces.