This textbook explores advanced topics in differential geometry,
chosen for their particular relevance to modern geometry
processing. Analytic and algebraic perspectives augment core
topics, with the authors taking care to motivate each new concept.
Whether working toward theoretical or applied questions, readers
will appreciate this accessible exploration of the mathematical
concepts behind many modern applications. Beginning with an
in-depth study of tensors and differential forms, the authors go on
to explore a selection of topics that showcase these tools. An
analytic theme unites the early chapters, which cover
distributions, integration on manifolds and Lie groups, spherical
harmonics, and operators on Riemannian manifolds. An exploration of
bundles follows, from definitions to connections and curvature in
vector bundles, culminating in a glimpse of Pontrjagin and Chern
classes. The final chapter on Clifford algebras and Clifford groups
draws the book to an algebraic conclusion, which can be seen as a
generalized viewpoint of the quaternions. Differential Geometry and
Lie Groups: A Second Course captures the mathematical theory needed
for advanced study in differential geometry with a view to
furthering geometry processing capabilities. Suited to classroom
use or independent study, the text will appeal to students and
professionals alike. A first course in differential geometry is
assumed; the authors' companion volume Differential Geometry and
Lie Groups: A Computational Perspective provides the ideal
preparation.
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