By J├│zsef Szilasi,Rezs┼æ L Lovas,D├ívid Cs Kert├⌐sz
This ebook presents a complete advent to Finsler geometry within the language of present-day arithmetic. via Finsler geometry, it additionally introduces the reader to different buildings and strategies of differential geometry.
Prerequisites for analyzing the e-book are minimum: undergraduate linear algebra (over the reals) and research. the required strategies and instruments of complex linear algebra (over modules), element set topology, multivariable calculus and the rudiments of the speculation of differential equations are built-in within the textual content. uncomplicated manifold and package theories are taken care of concisely, conscientiously and (apart from proofs) in a self-contained manner.
The spine of the publication is the specific and unique exposition of tangent package deal geometry, Ehresmann connections and sprays. It seems that those buildings are vital not just of their personal correct and within the beginning of Finsler geometry, yet they are often additionally considered as the cornerstones of the large edifice of Differential Geometry.
The authors emphasize the conceptual features, yet conscientiously intricate calculative features to boot (tensor derivations, graded derivations and covariant derivatives). even if they offer choice to index-free tools, in addition they practice the recommendations of conventional tensor calculus.
Most proofs are elaborated intimately, which makes the booklet compatible for self-study. however, the authors supply for extra complicated readers besides by means of providing them with sufficient fabric, and the publication can also function a reference.
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