Add this copy of The Differential Invariants of Generalized Spaces to cart. $29.95, good condition, Sold by CorgiPack rated 5.0 out of 5 stars, ships from Fulton, NY, UNITED STATES, published 1934 by The University press.
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Seller's Description:
Good. Ex-library book with expected library markings. In solid shape. From the Foreword: The impetus given within the last decade and a half by the theory of relativity to the study of generalized spaces and their differential invariants has resulted in many interesting and important discoveries in this field. Most important among these and most fruitful for later developments was the concept of the infinitesimal parallel displacement formulated by Levi-Civita in 1917-a concept which was soon extended by Weyl in the theory of the general affinely connected space. The discovery of the existence of a projective theory of the affinely connected space was made in 1921 by Weyl. This was followed by the discovery of the affine representation of the projective theory as well as of the conformal theory of metric spaces by the author. More general geometrical theories of projective space, intimately related to this anine representation, were devised by Schouten, Veblen and others. Also L. P. Eisenhart arrived at the idea of the invariant theory of the group space of an r-parameter continuous group, which was more fully developed by Cartan and Schouten. These and other researches in the theory of the differential invariants of generalized spaces, or as it is sometimes called, the absolute differential calculus, mark the period through which we have just passed. Further interesting results in this field undoubtedly await the investigations of the future. The following pages are intended to give the student a connected account, including the above recent developments, of the subject of the differential invariants of generalized spaces. It is my hope also that the book may be of some use to research workers. I have adopted the notation in most common use, which is undoubtedly the best. The book is exclusively analytical in character-above all I have striven for elegance of analytical procedure. Special geometrical points of view have been, as they should be, omitted, as such are primarily a matter of personal taste and should, in any case, be confined to books on geometry; I have thus excluded the viewpoint initiated by Cartan as well as the more recent geometrical formulations of Schouten and Veblen. While certain of the results given may possibly be included in the field of differential geometry, I have made no invasion of the strict province of this subject, i.e. the theory of curves and surfaces embedded in a space of higher dimensionality. 241 pages.
