Homogeneous Finsler Spaces is the first book to emphasize the
relationship between Lie groups and Finsler geometry, and the first
to show the validity in using Lie theory for the study of Finsler
geometry problems. This book contains a series of new results
obtained by the author and collaborators during the last decade.
The topic of Finsler geometry has developed rapidly in recent
years. One of the main reasons for its surge in development is its
use in many scientific fields, such as general relativity,
mathematical biology, and phycology (study of algae). This
monograph introduces the most recent developments in the study of
Lie groups and homogeneous Finsler spaces, leading the reader to
directions for further development. The book contains many
interesting results such as a Finslerian version of the
Myers-Steenrod Theorem, the existence theorem for invariant
non-Riemannian Finsler metrics on coset spaces, the Berwaldian
characterization of globally symmetric Finsler spaces, the
construction of examples of reversible non-Berwaldian Finsler
spaces with vanishing S-curvature, and a classification of
homogeneous Randers spaces with isotropic S-curvature and positive
flag curvature. Readers with some background in Lie theory or
differential geometry can quickly begin studying problems
concerning Lie groups and Finsler geometry.
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