Crate cartan_manifolds 

Concrete Riemannian manifold implementations.

Each manifold implements the traits from cartan-core using nalgebra SVector and SMatrix types for statically-sized storage.

Available manifolds

• Euclidean<N> – R^N with the flat metric (trivial baseline)
• Sphere<N> – S^{N-1} in R^N with round metric
• SpecialOrthogonal<N> – SO(N) with bi-invariant metric
• SpecialEuclidean<N> – SE(N) with product metric
• Corr<N> – Corr(N) correlation matrices with Frobenius metric (flat)
• Spd<N> – SPD(N) with affine-invariant metric (Cartan-Hadamard)
• Grassmann<N, K> – Gr(N, K) with canonical metric

no_std support

cartan-manifolds is no_std-compatible when the std feature is disabled:

cartan-manifolds = { version = "0.1", default-features = false, features = ["alloc"] }

Available without std (requires alloc): Euclidean<N>, Sphere<N>, SpecialOrthogonal<N>, SpecialEuclidean<N>, Grassmann<N, K>

Requires std (eigendecomposition or imports from qtensor): QTensor3, Corr<N>, Spd<N>, FrameField3D

Re-exports

pub use corr::Corr;

pub use euclidean::Euclidean;

pub use frame_field::FrameField3D;

pub use frame_field::d2_gauge_fix;

pub use grassmann::Grassmann;

pub use qtensor::QTensor3;

pub use se::SEPoint;

pub use se::SETangent;

pub use se::SpecialEuclidean;

pub use so::SpecialOrthogonal;

pub use spd::Spd;

pub use sphere::Sphere;

Modules

corr

Correlation matrix manifold Corr(N) with the Frobenius metric.

euclidean

Euclidean space R^N.

frame_field

Frame fields on nematic Q-tensor configurations.

grassmann

Grassmann manifold Gr(N, K) of K-dimensional subspaces of R^N.

qtensor

Q-tensor manifold: the space of 3×3 symmetric traceless matrices.

se

Special Euclidean group SE(N) — rigid motions in N dimensions.

so

Special orthogonal group SO(N) with the bi-invariant metric.

spd

Symmetric Positive Definite manifold SPD(N) with the affine-invariant metric.

sphere

Unit sphere S^{N-1} embedded in R^N.

util

Matrix utility functions shared across manifold implementations.