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**About this book :- **
**Tensors Mathematics of Differential Geometry and Relativity ** written by
** Zafar Ahsan**.

**Book Detail :- **
** Title: ** Tensors Mathematics of Differential Geometry and Relativity
** Edition: **
** Author(s): ** Zafar Ahsan
** Publisher: **
** Series: **
** Year: **
** Pages: ** 11
** Type: ** PDF
** Language: ** Englsih
** ISBN: **
** Country: **
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**Book Contents :- **
**Tensors Mathematics of Differential Geometry and Relativity ** written by
** Zafar Ahsan**
cover the following topics.
'
** Tensors and Their Algebra**

Introduction, Transformation of Coordinates, Summation Convention, Kronecker Delta, Scalar, Contravariant and Covariant Vectors, Tensors of Higher Rank, Symmetry of Tensors, Algebra of Tensors, Irreducible Tensor, Exercises
** Riemannian Space and Metric Tensor**

Introduction, The Metric Tensor, Raising and Lowering of Indices—Associated Tensor, Vector Magnitude, Relative and Absolute Tensors, Levi-Civita Tensor, Exercises
** Christoffel Symbols and Covariant Differentiation**

Introduction, Christoffel Symbols, Transformation Laws for Christoffel Symbols, Equation of a Geodesic, Affine Parameter, Geodesic Coordinate System, Covariant Differentiation, Rules for Covariant Differentiation, Some Useful Formulas, Intrinsic Derivative: Parallel Transport, Alternative Derivation of Equation of Geodesic, Exercises
** The Riemann Curvature Tensor**

Introduction, The Riemann Curvature Tensor, Commutation of Covariant Derivative: Another Way of Defining the Riemann Curvature Tensor, Covariant form of the Riemann Curvature Tensor, Properties of the Riemann Curvature Tensor, Uniqueness of Riemann Curvature Tensor, Number of Algebraically Independent Components of the Riemann Curvature Tensor, The Ricci Tensor and the Scalar Curvature, The Einstein Tensor, The Integrability of Riemann Tensor and the Flatness of the Space, Einstein Space, Curvature of a Riemannian Space, Spaces of Constant Curvature, Exercises
** Some Advanced Topics**

Introduction, Geodesic Deviation, Decomposition of Riemann Curvature Tensor, Electric and Magnetic Parts of the Riemann and Weyl Tensors, Classification of Gravitational Fields, Invariants of the Riemann Tensor, Lie Derivative, The Killing Equation, The Curvature Tensor and Killing Vectors, Curvature Tensors Involving Riemann Tensor, Exercises
** Applications**

Introduction, Maxwell’s Equations, Special Coordinate System, Energy-momentum Tensors, Kinematical Quantities—Raychaudhuri’s Equation, Solutions of Einstein Field Equations, Some Important Tensors
**Bibliography**
**Answers and Hints to Exercises**

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