The ISFMA-CIMPA School on "Differential Geometry: Theory and Applications" was held on 07 August-18 August 2006, in the building of the Chinese-French Institute for Applied Mathematics (ISFMA), Fudan University, Shanghai, China. This school was jointly organized by the ISFMA and the CIMPA (International Centre for Pure and Applied Mathematics), Nice, France. About sixty participants from China, Hong Kong, France, Cambodia, India, Iran, Pakistan, Philippines, Romania,Russia, Sri-Lanka, Thailand, Turkey, Uzbekistan and Vietnam attended this highly successful event.

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 book presents some important applications to shells,such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and mesh generation in finite element methods.

This volume will be very useful to graduate students and researchers in pure and applied mathematics.

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 G