3 Review(s)

This volume presents a collection of problemsand solutions in differential geometry withapplications. Both introductory and advancedtopics are introduced in an easy-to-digestmanner, with the materials of the volumebeing self-contained. In particular, curves,surfaces, Riemannian and pseudo-Riemannianmanifolds, Hodge duality operator, vectorfields and Lie series, differential forms, matrixvalueddifferential forms, Maurer–Cartanform, and the Lie derivative are covered.Readers will find useful applications to specialand general relativity, Yang–Mills theory,hydrodynamics and field theory. Besidesthe solved problems, each chapter containsstimulating supplementary problems andsoftware implementations are also included.The volume will not only benefit studentsin mathematics, applied mathematics andtheoretical physics, but also researchers in thefield of differential geometry.