This monograph is a detailed survey of an area of differential geometry surrounding the Bochner technique.This is a technique that falls
　　under the general heading of"curvature and topology"and refers to a method initiated by Salomon Bochner in the 1940's for proving on compact Riemannian manifolds that certain objects of geometric interest(e.g.harmonic forms,harmonic spinor fields,etc.)must satisfy additional differential equations when appropriate curvatureconditions are imposed.In 1953,K.Kodaira applied this method to prove the vanishing theorem that now bears his name for harmonic forms with values in a holomorphic vector bundle;this was the crucial step that allowed him to prove his famous imbedding theorem.Subsequently,the Bochner technique has been extended,on the one hand,to spinor fields andharmonic maps and,on the other,to harmonic functions and harmonic maps on noncompact manifolds.The last has led to the proof of rigidity properties of certain Kähler manifolds and locally symmetric spaces.This monograph gives a self-contained and coherent account of some of these developments,assuming the basic facts about Riemannian and Kähler geometry as well as the statement of the Hodge theorem.Thebrief introductions to the elementary portions of spinor geometry and harmonic maps may be especially useful to beginners.
　　Bochner技術(shù)是數(shù)學(xué)中經(jīng)典和有效的技術(shù)，可以用來證明數(shù)學(xué)中非常重要的消失定理和剛性性質(zhì)。伍鴻熙教授著書眾多，寫作經(jīng)驗豐富，本書是di一次系統(tǒng)介紹Bochner技術(shù)及其應(yīng)用的著作。