From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices provide background information on point set topology, calculus of variations, and multilinear algebra—topics that may not have been covered in the prerequisite courses of multivariable calculus and linear algebra.

Differential Geometry of Manifolds takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics, including the Hamiltonian formulation of dynamics (with a view toward symplectic manifolds), the tensorial formulation of electromagnetism, some string theory, and some fundamental concepts in general relativity.

Reviews

Differential Geometry of Curves and Surfaces and Differential Geometry of Manifolds will certainly be very useful for many students. A distinguishing feature of the books is that many of the basic notions, properties and results are illustrated by a great number of examples and figures. Each section includes numerous interesting exercises, which make these books ideal for self-study too. These books give a nice addition to the existing literature in the field of differential geometry of curves, surfaces, and manifolds. I strongly recommend them to anyone wishing to enter into the beautiful world of the differential geometry.

—Velichka Milousheva, Journal of Geometry and Symmetry in Physics, 2012

It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. … The book takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics…

—L’Enseignement Mathé (2) 57 (2011)

Lovett fills with this book a blatant gap in the vast collection of books on differential geometry. The book is easily accessible for students with a basic understanding of partial derivatives and a basic knowledge of vector spaces. …

it provides a thorough understanding of the most important concepts and thus opens the way for further studies, either in differential geometry (many references to other textbooks that go deeper into the subjects are included in the book) or in other research areas where differential geometry provides the language and tools to describe and solve the area’s problems. An ample number of examples and exercises stimulate mastery in handling the tools introduced in the text.

The book is well suited for an introductory course in differential geometry, graduate students in mathematics or other sciences (physics, engineering, biology) who need to master the differential geometry of manifolds as a tool, or any mathematician who lik...