โ Scribed by Oswald Veblen, J. H. C. Whitehead
No coin nor oath required. For personal study only.
This book contains a set of axioms for differential geometry and develops their consequences up to a point where a more advanced book might reasonably begin. Analytical operations with co-ordinate systems are continually used in differential geometry, a typical process being to 'choose a co-ordinate system such that ...' It is therefore natural to state the axioms in terms of an undefined class of 'allowable' co-ordinate systems, and to deduce the properties of the space from the nature of the transformations of co-ordinates permitted by the axioms. These earlier axioms are found to be adequate for the differential geometry of an open simply connected space, the most elementary theorems of which occupy the greater part of Chapters III-V. The more general axioms, in terms of allowable co-ordinate systems and without restrictions on the connectivity of the space, are given in Chapter IV.
๐ SIMILAR VOLUMES
These notes are from a lecture course "Differentialgeometrie und Lie Gruppen" which has been held at the University of Vienna during the academic year 1990/91, again in 1994/95, and in WS 1997. It is not yet complete and will be enlarged during the year.In this lecture course I give complete definit