christoffel_n.hpp File Reference

Christoffel symbol computation for an NAssetManifold. More...

#include "n_asset_manifold.hpp"
#include <optional>
#include <vector>
#include <Eigen/Dense>

Go to the source code of this file.

Classes
class	srfm::tensor::ChristoffelN
	Computes Christoffel symbols Γ^λ_μν for an NAssetManifold. More...

Namespaces
namespace	srfm
namespace	srfm::tensor

Detailed Description

Christoffel symbol computation for an NAssetManifold.

Module: include/srfm/tensor/ Stage: 4 — N-Asset Manifold

Responsibility

Compute the Christoffel symbols of the second kind,

Γ^λ_μν = ½ g^λσ (∂_μ g_νσ + ∂_ν g_μσ - ∂_σ g_μν)

for an arbitrary NAssetManifold via central finite-differences on the metric tensor.

Guarantees

• Thread-safe: ChristoffelN is stateless beyond holding a const reference to the manifold.
• All fallible operations return std::optional.
• All public methods are noexcept.
• For a constant metric (flat manifold) all symbols are exactly zero.

NOT Responsible For

• Second derivatives / Riemann tensor.
• Geodesic integration (see geodesic_n.hpp).

Definition in file christoffel_n.hpp.