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This subtopic introduces the core ideas in local differential geometry, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Linear and affine connections. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Projective connections. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Differential geometric aspects of statistical manifolds. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Other connections. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Local Riemannian geometry. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Methods of Riemannian geometry. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Local submanifolds. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Local theory of Lorentzian metrics and connections. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Hermitian and Kählerian structures. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Finsler spaces and generalizations (areal metrics). This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.
Applications of local differential geometry to the sciences. This topic develops local differential geometry of manifolds, connections, and curvature tensors in smooth settings.
Wikipedia: Riemannian geometry
Used to formulate and analyze geometric PDEs and local metric invariants on smooth manifolds.