Ehresmann curvature

Target entity: Ehresmann curvature
Context triple: [Ehresmann connection, hasCurvature, Ehresmann curvature]

• A. Ehresmann connection
  An Ehresmann connection is a geometric structure on a fiber bundle that specifies a way to consistently split tangent spaces into vertical and horizontal parts, enabling the definition of parallel transport.
• B. Cartan connections
  Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
• C. Maurer–Cartan form
  The Maurer–Cartan form is a canonical Lie algebra-valued 1-form on a Lie group that encodes its infinitesimal structure and underlies many constructions in differential geometry and gauge theory.
• D. Oka–Cartan theory
  Oka–Cartan theory is a foundational area of complex analysis that studies the structure and properties of holomorphic functions and coherent analytic sheaves on complex manifolds, particularly Stein spaces.
• E. Riemann curvature tensor
  The Riemann curvature tensor is a fundamental geometric object in differential geometry that measures how much a Riemannian manifold deviates from being flat by encoding the intrinsic curvature of the space.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Ehresmann curvature
Target entity description: Ehresmann curvature is the geometric object that measures the failure of horizontal distributions in an Ehresmann connection to be integrable, capturing how parallel transport around infinitesimal loops deviates from being path-independent.

• A. Ehresmann connection
  An Ehresmann connection is a geometric structure on a fiber bundle that specifies a way to consistently split tangent spaces into vertical and horizontal parts, enabling the definition of parallel transport.
• B. Cartan connections
  Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
• C. Maurer–Cartan form
  The Maurer–Cartan form is a canonical Lie algebra-valued 1-form on a Lie group that encodes its infinitesimal structure and underlies many constructions in differential geometry and gauge theory.
• D. Oka–Cartan theory
  Oka–Cartan theory is a foundational area of complex analysis that studies the structure and properties of holomorphic functions and coherent analytic sheaves on complex manifolds, particularly Stein spaces.
• E. Riemann curvature tensor
  The Riemann curvature tensor is a fundamental geometric object in differential geometry that measures how much a Riemannian manifold deviates from being flat by encoding the intrinsic curvature of the space.
• F. None of above. chosen