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By Andrey Popov

This monograph offers the elemental strategies of hyperbolic Lobachevsky geometry and their attainable purposes to fashionable nonlinear utilized difficulties in arithmetic and physics, summarizing the findings of approximately the final hundred years. The vital sections hide the classical development blocks of hyperbolic Lobachevsky geometry, pseudo round surfaces concept, internet geometrical investigative strategies of nonlinear differential equations in partial derivatives, and their functions to the research of the actual types. because the sine-Gordon equation looks to have profound “geometrical roots” and diverse purposes to trendy nonlinear difficulties, it really is handled as a common “object” of research, connecting a few of the difficulties mentioned.

The objective of this publication is to shape a common geometrical view at the assorted difficulties of contemporary arithmetic, physics and common technology normally within the context of non-Euclidean hyperbolic geometry.

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