CHAPTER 11: EUCLIDEAN THREE-DIMENSIONAL SPACES

The following sections are included:

• Definition of Homogeneous Fields in Euclidean Three-Space

• Curvature Form

• Jacobi Identity

• Classification of Homogeneous Fields

• Euclidean Three-Space

• Curvature Form Calculation

• Riemann Tensor

• Ricci Tensor

• Ricci Tensor Eigenvectors (c_r ≠ 0)

• Ricci Tensor Eigenvectors (c_r = 0)

• Homogeneous Field Components

• Ricci Tensor in Field Strengths

• Ricci Tensor (continued)

• Homogeneous Gravitational Fields in Euclidean ℝ³

• ADDENDUM: Ricci Tensor Calculation from Field Strengths

• ADDENDUM: Ricci Tensor and Ricci Coefficients - The Vector Free Case