Aspects of Differential Geometry III (Synthesis Lectures on Mathematics and Statistics)

Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, Jeong Hyeong Park, Ramón Vázquez-Lorenzo

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商品描述

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book III is aimed at the first-year graduate level but is certainly accessible to advanced undergraduates. It deals with invariance theory and discusses invariants both of Weyl and not of Weyl type; the Chern‒Gauss‒Bonnet formula is treated from this point of view. Homothety homogeneity, local homogeneity, stability theorems, and Walker geometry are discussed. Ricci solitons are presented in the contexts of Riemannian, Lorentzian, and affine geometry.

商品描述(中文翻譯)

微分幾何是一個廣泛的領域。我們選擇專注於某些適合入門的方面,並沒有試圖進行百科全書式的處理。第三冊適用於研究生的第一年級水平,但對高年級本科生也是可理解的。它涉及不變理論,並討論了韋爾型和非韋爾型的不變量;從這個角度來看,處理了切爾‒高斯‒博奈特公式。討論了相似性均勻性、局部均勻性、穩定性定理和沃克幾何。在黎曼、洛倫茲和仿射幾何的背景下介紹了里奇溶子。