Riemannian geometry. (English) Zbl 0041.29403

Princeton: Princeton University Press. vii, 306 p. (1949).
See the review of the first ed. (1926) in JFM 52.0721.01 (joint review in JFM 52.0721.02).
In this printing, errata in previous editions have been corrected in the text. Other revisions are in the appendix (37 pages), which also contains new material. There is an additional bibliography but the index does not include the appendix.
From the new material we mention the expression of the metric tensor in terms of normal coordinates; the canonical forms of the metric tensor of a \(V_n\) which admits \(r\) independent fields of parallel vectors; the orthogonal coordinate systems of Stäckel; spaces \(V_n\) of class greater than 1; the normal complexes of a \(V_n\) in \(R_m\); a theorem of T. Y. Thomas concerning a \(V_n\), \(n>3\), of class one; Einstein spaces of class one for \(n\ge 4\); the independent infinitesimal conformal transformations of a \(V_3\) and of a conformally flat \(V_n\), \(n>3\); and the \(V_n\) admitting a simply transitive group of motions.
Reviewer: J. A. Schouten


53-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry
53Cxx Global differential geometry