Geometrical Properties Of Vectors And Covectors: An Introductory Survey Of Differentiable Manifolds, Tensors And Forms An Introductory Survey of Differentiable Manifolds, Tensors and Forms

This is a brief introduction to some geometrical topics including topological spaces, the metric tensor, Euclidean space, manifolds, tensors, r-forms, the orientation of a manifold and the Hodge star operator. It provides the reader who is approaching the subject for the first time with a deeper understanding of the geometrical properties of vectors and covectors. The material prepares the reader for discussions on basic concepts such as the differential of a function as a covector, metric dual, inner product, wedge product and cross product. J M Domingos received his D Phil from the University of Oxford and has now retired from the post of Professor of Physics at the University of Coimbra, Portugal.

this Is A Brief Introduction To Some Geometrical Topics Including Topological Spaces, The Metric Tensor, Euclidean Space, Manifolds, Tensors, R-forms, The Orientation Of A Manifold And The Hodge Star Operator. It Provides The Reader Who Is Approaching The Subject For The First Time With A Deeper Understanding Of The Geometrical Properties Of Vectors And Covectors. The Material Prepares The Reader For Discussions On Basic Concepts Such As The Differential Of A Function As A Covector, Metric Dual, Inner Product, Wedge Product And Cross Product.

about The Author:
j M Domingos Retired From The Post Of Professor Of Physics At The University Of Coimbra, Portugal

This is a brief introduction to some geometrical topics including topological spaces, the metric tensor, Euclidean space, manifolds, tensors, r- forms, the orientation of a manifold and the Hodge star operator. It provides the reader who is approaching the subject for the first time with a deeper understanding of the geometrical properties of vectors and covectors. The material prepares the reader for discussions on basic concepts such as the differential of a function as a covector, metric dual, inner product, wedge product and cross product. J M Domingos received his D Phil from the Universi Contents......Page 8 Preface......Page 6 1. Topological Spaces......Page 9 2. Metric Tensor......Page 15 3.1 Basic definitions......Page 21 3.2 Tangent vectors and spaces......Page 25 3.3 Parallelization......Page 32 4. Metric Dual......Page 35 5. Tensors......Page 47 6. r-Forms......Page 53 7. Orientation of a Manifold......Page 63 8. Hodge Star Operator......Page 69 9. Wedge Product and Cross Product......Page 73 Bibliography......Page 77 Index......Page 79 Provides a brief introduction to some geometrical topics including topological spaces, the metric tensor, Euclidean space, manifolds, tensors, r-forms, and more. This book prepares the reader for discussions on basic concepts such as the differential of a function as a covector, metric dual, inner product, wedge product and cross product. 1. Topological spaces -- 2. Metric tensor -- 3. Differentiable manifolds. 3.1 Basic definitions. 3.2. Tangent vectors and spaces. 3.3. Parallelization -- 4. Metric dual -- 5. Tensors -- 6. r-Forms -- 7. Orientation of a manifold -- 8. Hodge star operator -- 9. Wedge product and cross product