SUMMARY
The discussion centers on the need for a citeable source that provides the formula for Gaussian curvature at a point on an intrinsically defined Riemannian or Semi-Riemannian manifold, specifically using the intrinsic metric tensor or Riemann tensor. The user seeks a professionally published journal or textbook source, as existing sources are not permissible for citation. The focus is on coordinate-based formulas, particularly in Ricci-style notation, suitable for computational approaches that require explicit mathematical formulations for algorithm development.
PREREQUISITES
- Understanding of Riemannian and Semi-Riemannian manifolds
- Familiarity with Gaussian curvature and its computation
- Knowledge of intrinsic metric tensors and Riemann tensors
- Proficiency in Ricci calculus and debauch-of-indices notation
NEXT STEPS
- Research "Gaussian curvature in Riemannian geometry" for foundational knowledge
- Explore "Ricci calculus" for understanding coordinate-based formulations
- Investigate "published sources on Riemannian geometry" for citation purposes
- Learn about "computational methods in differential geometry" for algorithm development
USEFUL FOR
Mathematicians, physicists, and computer scientists involved in differential geometry, particularly those developing algorithms based on Riemannian metrics and Gaussian curvature calculations.