The purpose of this book is to bridge the gap between differential geometry of Euclidean space of three dimensions and the more advanced work on differential geometry of generalised space. The subject is treated with the aid of the Tensor Calculus, which is associated with the names of Ricci and Levi-Civita; and the book provides an introduction both to this calculus and to Riemannian geometry. The geometry of subspaces has been considerably simplified by use of the generalized covariant differentiation introduced by Mayer in 1930, and successfully applied by other mathematicians.
The purpose of this book is to bridge the gap between differential geometry of Euclidean space of three dimensions and the more advanced work on differential geometry of generalised space. The subject is treated with the aid of the Tensor Calculus, which is associated with the names of Ricci and Levi-Civita; and the book provides an introduction both to this calculus and to Riemannian geometry. The geometry of subspaces has been considerably simplified by use of the generalized covariant differentiation introduced by Mayer in 1930, and successfully applied by other mathematicians.
1. Some Preliminaries; 2. Coordinates, Vectors , Tensors; 3. Riemannian Metric; 4. Christoffel's Three-Index Symbols. Covariant Differentiation; 5. Curvature of a Curve. Geodeics, Parallelism of Vectors; 6. Congruences and Orthogonal Ennuples; 7. Riemann Symbols. Curvature of a Riemannian Space; 8. Hypersurfaces; 9. Hypersurfaces in Euclidean Space. Spaces of Constant Curvature; 10. Subspaces of a Riemannian Space.
The purpose of this book is to bridge the gap between differential geometry of Euclidean space of three dimensions and differential geometry of generalised space.
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