分析、流形和物理学

we are happy that the success of the first edition gave us a chance to prepare a revised edition. we have made numerous changes and added exercises with their solutions to ease the study of several chapters. the major addition is a chapter "connections on principal fibre bundles" which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, mono poles, instantons, spin structure and spin connections. other additions include a section on the second fundamental form, a section on almost complex and kiihlerian manifolds, and a problem on the method of stationary phase. more than 150 entries have been added to the index. 　　can this book, now polished by usage, serve as a text for an advanced physical mathematics course this question raises another question what is the function of a text book for graduate studies in our times of rapidly expanding knowledge, a teacher looks for a book which will provide a broader base for future developments than can be covered in one or two semesters of lectures and a student hopes that his purchase will serve him for many years. a reference book which can be used as a text is an answer to their needs. this is what this book is intended to be, and thanks to a publishing company which keeps it moderately priced, this is what we hope it will he.