Quite simply, this book offers the most comprehensive survey to
date of the theory of semiparallel submanifolds. It begins with the
necessary background material, detailing symmetric and
semisymmetric Riemannian manifolds, smooth manifolds in space
forms, and parallel submanifolds. The book then introduces
semiparallel submanifolds and gives some characterizations for
their class as well as several subclasses. The coverage moves on to
discuss the concept of main symmetric orbit and presents all known
results concerning umbilic-like main symmetric orbits. With more
than 40 published papers under his belt on the subject, Lumiste
provides readers with the most authoritative treatment.
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