Isbn: 9781332040353 - on a category of transformation groups in three and four dimensions: inaugural dissertation, submitted to the philosophical faculty of the university ... of doctor of philosophy (classic reprint) (3 risultati)

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

Paperback. Condizione: New. Print on Demand. This book explores the development and capabilities of a particular category of transformation groups in three and four dimensions. The author was guided by the respected mathematician Sophus Lie. It begins with Riemann's foundational work on the geometry of multiple dimensions, which is further developed by Helmholtz. The author focuses on a theorem proposed by Lie, which attempts to identify transformation groups that preserve the geometric properties of a rigid body in space, while considering various interpretations of Helmholtz's axiom of unrestricted motion. The text thoroughly examines the eight groups that satisfy the given conditions, discussing their one-parametric subgroups and the behavior of points under specific constraints. A notable finding is that some groups exhibit closed path-curves under certain conditions, while others do not. Overall, this book provides a detailed analysis of transformation groups in multiple dimensions, expanding on Lie's work and contributing to the understanding of geometric transformations in higher dimensions. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item.…