Lectures on Differential Geometry

Advances in technology over the last 25 years have created a situation in which workers in diverse areas of computerscience and engineering have found it neces­ sary to increase their knowledge of related fields in order to make further progress. Clifford (geometric) algebra offers a unified algebraic framework for the direct expression of the geometric ideas underlying the great mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry.

This volume is based on the lectures given at the First Inter University Graduate School on Gravitation and Cosmology organized by IUCAA, Pune, in 1989. This series of Schools have been carefully planned to provide a sound background and preparation for students embarking on research in these and related topics. Consequently, the contents of these lectures have been meticulously selected and arranged. The topics in the present volume offer a firm mathematical foundation for a number of subjects to be de­ veloped later. These include Geometrical Methods for Physics, Quantum Field Theory Methods and Relativistic Cosmology.

These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases.