This book gives the basic notions of differential geometry,such as the metric tensor, the Riemann curvature tensor,the fundamental forms of a surface, covariant derivatives,and the fundamental theorem of surface theory in a self-contained and accessible manner. Although the field is often considered a "classical" one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role.
The ISFMA-CIMPA School on"Differential Geometry:Theory andApplications"was held on 07 August-18 August 2006，in the building ofthe Chinese-French Institute for Applied Mathematics（ISFMA）,FudanUniversity,Shanghai,China.This school was jointly organized by theISFMA and the CIMPA（International Centre for Pure and AppliedMathematics）,Nice,France.About sixty participants from China,HongKong,France,Cambodia,India,Iran,Pakistan,Philippines,Romania,Russia,Sri-Lanka,Thailand,Turkey,Uzbekistan and Vietnam attendedthis highly successful event.
The first objective of this school was to lay down in a self-contained:and accessible manner the basic notions of differential geometry,suchasthe metric tensor,the Riemann curvature tensor,the fundamental formsof a surface,covariant derivatives,and the fundamental theorem of sur-face theory etc.Although this field is with good reasons often consideredas a"classical"one,it has been recently"rejuvenated",thanks to themanifold applications where it plays an essential role.
The second objective of this school was to present some of theseapplications,such as the theory of linearly and nonlinearly elastic shells,the implementation of numerical methods for shells,and mesh generationin finite element methods.
To fulfill these objectives,four series of lectures,each series compris-ing ten 50min-lectures,were delivered under the following titles:"In-troduction to differential geometry","Introduction to shell theory","Adifferential geometry approach to mesh generation",and"Numericalmethods for shells".This volume gathers the materials covered in theselectures.As such,this volume should be very useful to graduate studentsand researchers in pure and applied mathematics.
The organizers take pleasure in thanking the various organizations fortheir generous support:The ISFMA,the CIMPA,the French Embassyin Beijing,the Consulate General of France in Shanghai,the NationalNatural Science Foundation of China,Fudan University,Higher Educa-tion Press and World Scientific.Finally,our special thanks are due toMrs.Zhou Chun-Lian for her patient and effective work in editing thisbook.
李大潜，数学家。江苏南通人。1957年毕业于复旦大学数学系，1966年该校在职研究生毕业。1997年当选为第三世界科学院院士。复旦大学教授。中国工业与应用数学学会理事长，中国数学会副理事长，中法应用数学研究所所长。对一般形式的二自变数拟线性双曲型方程组的自由边界问题和间断解的系统研究，以及对非线性波动方程经典解的整体存在性及生命跨度的完整结果，均处于国际领先地位，得到国际上的高度评价。在理论研究的基础上，对各种电阻率测井建立了统一的数学模型和方法，并成功地在国内10多个油田推广使用。1995年当选为中国科学院院士。
Preface
Philippe G. Ciarlet: An Introduction to Differential Geometry in R 3
Philippe G. Ciarlet, Cristinel Mardare: An Introduction to Shell Theory
Dominique Chapelle: Some New Results and Current Challenges in the Finite Element Analysis of Shells
Pascal Frey: A Differential Geometry Approach to Mesh Generation
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