Riemannian Geometry in an Orthogonal Fra
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Om Riemannian Geometry in an Orthogonal Fra
Foreword by S S Chern In 1926–27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fiber bundle of a submanifold, etc. It has now been translated into eng by Vladislav V Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who also edited the Russian edition.Contents:Method of Moving FramesThe Theory of Pfaffian FormsIntegration of Systems of Pfaffian Differential EquationsGeneralizationThe Existence Theorem for a Family of Frames with Given Infinitesimal Components ωi and ωijThe Fundamental Theorem of Metric GeometryVector Analysis in an n-Dimensional Euclidean SpaceThe Fundamental Principles of Tensor AlgebraTensor AnalysisThe Notion of a ManifoldLocally Euclidean Riemannian ManifoldsEuclidean Space Tangent at a PointOsculating Euclidean SpaceEuclidean Space of Conjugacy Along a LineSpace with a Euclidean ConnectionRiemannian Curvature of a ManifoldSpaces of Constant CurvatureGeometric Construction of a Space of Constant CurvatureVariational Problems for GeodesicsDistribution of Geodesics Near a Given GeodesicGeodesic SurfacesLines in a Riemannian ManifoldSurfaces in a Three-Dimensional Riemannian ManifoldForms of Laguerre and Darbouxp-Dimensional Submanifolds in a Riemannian Manifold of n DimensionsReadership: Senior undergraduates, graduate students and researchers in geometry and topology.Key Features:There is no single book comprehensively covering all these topics currently available in the market todayProvides current standing in the field of carbon nanomaterials and their applicationsCovers research on wide variety of carbon materials, including, fullerenes, endohedral fullerenes, organofullerenes, nanotubes and related structures, graphene, etc.Nanotechnology aspects of carbon based materials