The book aims to present a comprehensive survey on biharmonic
submanifolds and maps from the viewpoint of Riemannian geometry. It
provides some basic knowledge and tools used in the study of the
subject as well as an overall picture of the development of the
subject with most up-to-date important results.Biharmonic
submanifolds are submanifolds whose isometric immersions are
biharmonic maps, thus biharmonic submanifolds include minimal
submanifolds as a subclass. Biharmonic submanifolds also appeared
in the study of finite type submanifolds in Euclidean
spaces.Biharmonic maps are maps between Riemannian manifolds that
are critical points of the bienergy. They are generalizations of
harmonic maps and biharmonic functions which have many important
applications and interesting links to many areas of mathematics and
theoretical physics.Since 2000, biharmonic submanifolds and maps
have become a vibrant research field with a growing number of
researchers around the world, with many interesting results have
been obtained.This book containing basic knowledge, tools for some
fundamental problems and a comprehensive survey on the study of
biharmonic submanifolds and maps will be greatly beneficial for
graduate students and beginning researchers who want to study the
subject, as well as researchers who have already been working in
the field.
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