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Differential Geometry of Curves and Surfaces with Singularities (Hardcover)
Loot Price: R3,525
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Differential Geometry of Curves and Surfaces with Singularities (Hardcover)
Series: Series in Algebraic and Differential Geometry, 1
Expected to ship within 10 - 15 working days
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This book provides a unique and highly accessible approach to
singularity theory from the perspective of differential geometry of
curves and surfaces. It is written by three leading experts on the
interplay between two important fields — singularity theory and
differential geometry. The book introduces singularities and their
recognition theorems, and describes their applications to geometry
and topology, restricting the objects of attention to singularities
of plane curves and surfaces in the Euclidean 3-space. In
particular, by presenting the singular curvature, which originated
through research by the authors, the Gauss–Bonnet theorem for
surfaces is generalized to those with singularities. The
Gauss–Bonnet theorem is intrinsic in nature, that is, it is a
theorem not only for surfaces but also for 2-dimensional Riemannian
manifolds. The book also elucidates the notion of Riemannian
manifolds with singularities. These topics, as well as elementary
descriptions of proofs of the recognition theorems, cannot be found
in other books. Explicit examples and models are provided in
abundance, along with insightful explanations of the underlying
theory as well. Numerous figures and exercise problems are given,
becoming strong aids in developing an understanding of the
material. Readers will gain from this text a unique introduction to
the singularities of curves and surfaces from the viewpoint of
differential geometry, and it will be a useful guide for students
and researchers interested in this subject.
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