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The Differential Geometry of Finsler Spaces (Paperback, Softcover reprint of the original 1st ed. 1959)
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The Differential Geometry of Finsler Spaces (Paperback, Softcover reprint of the original 1st ed. 1959)
Series: Grundlehren der mathematischen Wissenschaften, 101
Expected to ship within 10 - 15 working days
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The present monograph is motivated by two distinct aims. Firstly,
an endeavour has been made to furnish a reasonably comprehensive
account of the theory of Finsler spaces based on the methods of
classical differential geometry. Secondly, it is hoped that this
monograph may serve also as an introduction to a branch of
differential geometry which is closely related to various topics in
theoretical physics, notably analytical dynamics and geometrical
optics. With this second object in mind, an attempt has been made
to describe the basic aspects of the theory in some detail - even
at the expense of conciseness - while in the more specialised
sections of the later chapters, which might be of interest chiefly
to the specialist, a more succinct style has been adopted. The fact
that there exist several fundamentally different points of view
with regard to Finsler geometry has rendered the task of writing a
coherent account a rather difficult one. This remark is relevant
not only to the development of the subject on the basis of the
tensor calculus, but is applicable in an even wider sense. The
extensive work of H. BUSEMANN has opened up new avenues of approach
to Finsler geometry which are independent of the methods of
classical tensor analysis. In the latter sense, therefore, a full
description of this approach does not fall within the scope of this
treatise, although its fundamental l significance cannot be
doubted.
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