chapter  8
20 Pages

Bundles and tensors

WithMichael K. Murray, John W. Rice

So far we have managed to avoid mentioning two of differential geometry’s most useful concepts, vector bundles and principal bundles. Vector and principal bundles are generalisations of the tangent bundle bundle of a manifold. We want to discuss them now partly for the sake of completeness but more because they enable us to give a definition of tensor which is readily generalised in our final chapter to higher-order constructions such as strings.