By Vladislav V Goldberg, Shiing-Shen Chern

Foreword through S S Chern

In 1926-27, Cartan gave a chain of lectures within which he brought external types on the very starting and used greatly orthogonal frames all through to enquire the geometry of Riemannian manifolds. during this path he solved a chain of difficulties in Euclidean and non-Euclidean areas, in addition to a sequence of variational difficulties on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of those Cartan's lectures and released them as a booklet entitled Riemannian Geometry in an Orthogonal body. This ebook has many inventions, akin to the concept of intrinsic common differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional area or in an area of continuous curvature, an affine connection outlined in a typical fiber package deal of a submanifold, and so forth. It has now been translated into English via Vladislav V Goldberg, presently unique Professor of arithmetic on the New Jersey Institute of expertise, united states, who additionally edited the Russian version.