Title: On a Category of Transformation Groups in Three and Four Dimensions: Inaugural Dissertation, Submitted to the Philosophical Faculty of the University of Leipzig for the Degree of Doctor of Philosophy (Classic Reprint)
Publisher: Forgotten Books
Publication Date: 2018
Language: English
ISBN 10: 0267684533
ISBN 13: 9780267684533
Binding: HRD
Condition: New
Weight: 265 grams

About this title

Synopsis

A rigorous study of transformation groups in three and four dimensions, showing how key axioms shape which movements are possible and how invariants arise.

In inaugural dissertation format, it surveys the development started by Helmholtz and refined by Lie, with extensions by Kowalewski to higher dimensions. The work focuses on six‑parametric groups in space and the special surfaces and path�curves that arise when certain points are held fixed. It blends historical context with detailed group-theoretic analysis to reveal the structure of space under these transformations.

Explains Helmholtz’s axioms and Lie’s conclusions about six-parameter groups in three and four dimensions.
Investigates invariant surfaces, pseudospheres, and the behavior of path-curves under different subgroups.
Describes imprimitive and primitive group cases and how they affect invariants and transitivity.
Presents explicit group constructions and their geometric interpretations in space and higher dimensions.

Ideal for readers of advanced mathematics and the history of geometry who want a careful, scholarly treatment of transformation groups.

nonfiction

"About this title" may belong to another edition of this title.

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