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A manifold locally modeled on complex Euclidean space with holomorphic transition maps.
wp-complex-manifoldnlab-complex-manifoldlee-smooth-manifoldsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Choose complex charts with holomorphic transition maps.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-complex-manifoldlee-smooth-manifoldsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Supply the Complex manifold structure as one jointly required input.
Feed several structures into a construction junction and impose compatibility between them.
wp-hermitian-manifoldnlab-hermitian-manifoldlee-smooth-manifoldslee-riemannian-manifoldsThis is an authored directed relation from the source endpoint to the target endpoint.
Holomorphic transition maps are smooth, so a complex atlas canonically determines an underlying smooth manifold of twice the complex dimension.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-complex-manifoldnlab-smooth-manifoldlee-smooth-manifolds