Geometrical Methods in Physics
Charlie Harper · 1999
This chapter contains sections titled: Introduction Transformation of Coordinates in Linear Spaces Contravariant and Covariant Tensors Tensors of Rank One Higher-Rank Tensors Symmetric and Antisymmetric Tensors Polar and Axial Vectors Tensor Algebra Addition (Subtraction) Multiplication (Outer Product) Contraction Inner Product The Quotient Law The Line Element The Fundamental Metric Tensor Associate Tensors Tensor Calculus Introduction Christoffel Symbols Covariant Differentiation of Tensors The Equation of the Geodesic Line Special Equations Involving the Metric Tensor The Riemann-Christoffel Tensor The Curvature Tensor The Ricci Tensor The Einstein Tensor and Equations of General Relativity Exterior Differential Forms Introduction Exterior Product Exterior Derivative The Exterior Product and Exterior Derivative in ℜ3 The Generalized Stokes Theorem Problems