By J├│zsef Szilasi,Rezs┼æ L Lovas,D├ívid Cs Kert├⌐sz
This ebook presents a finished advent to Finsler geometry within the language of present-day arithmetic. via Finsler geometry, it additionally introduces the reader to different constructions and methods of differential geometry.
Prerequisites for analyzing the booklet are minimum: undergraduate linear algebra (over the reals) and research. the required options and instruments of complicated linear algebra (over modules), element set topology, multivariable calculus and the rudiments of the idea of differential equations are built-in within the textual content. uncomplicated manifold and package theories are taken care of concisely, rigorously and (apart from proofs) in a self-contained manner.
The spine of the publication is the certain 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 complex calculative points to boot (tensor derivations, graded derivations and covariant derivatives). even supposing they provide choice to index-free equipment, in addition they follow 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 complex readers besides by means of offering them with sufficient fabric, and the publication can also function a reference.
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