Riemannian Geometry (dhl)

Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text.

A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.

《黎曼幾何學》是一本廣受好評且成功的教科書的擴充版（最初以葡萄牙語出版），專為數學和物理學的研究生一年級學生而設計。作者的教學方法直接進入黎曼幾何的基本語言，並立即呈現一些最基本的定理。這本書的內容很基礎，只需要讀者具備一些基本背景知識，因此適合各種不同的學生和課程結構。曾使用過這本教材的教師們稱其選題「出色」。

這本書的一個重要特點是其強大且具啟發性的結構，從定義可微流形開始，一直到黎曼幾何學中最重要的結果之一——球面定理的證明。這本書充滿了基本定義和定理、例子、應用以及大量的練習題，以測試學生的理解能力，並擴展對這一主題的知識和洞察力。教師和學生都會發現這本書對這個高度實用且激動人心的學科做出了重要貢獻。