Gauss map

Target entity: Gauss map
Context triple: [Khinchin–Lévy constant, relatedConcept, Gauss map]

• A. Gauss map
  The Gauss map is a differential geometry concept that assigns to each point on a surface the corresponding point on the unit sphere determined by the surface’s normal vector at that point.
• B. Weingarten map
  The Weingarten map is a differential geometric operator on a surface that encodes how the surface’s normal vector field changes, thereby describing the surface’s extrinsic curvature.
• C. Gaussian curvature
  Gaussian curvature is a fundamental concept in differential geometry that measures how a surface bends at a point by combining its principal curvatures into a single intrinsic quantity.
• D. Gauss–Codazzi equations
  The Gauss–Codazzi equations are fundamental compatibility conditions in differential geometry that relate the intrinsic curvature of a surface to its extrinsic curvature as embedded in a higher-dimensional space.
• E. Theorema Egregium
  Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Gauss map
Target entity description: The Gauss map is a transformation on the unit interval that sends a real number to the fractional part of its reciprocal and underlies the dynamics of continued fraction expansions.

• A. Gauss map
  The Gauss map is a differential geometry concept that assigns to each point on a surface the corresponding point on the unit sphere determined by the surface’s normal vector at that point.
• B. Weingarten map
  The Weingarten map is a differential geometric operator on a surface that encodes how the surface’s normal vector field changes, thereby describing the surface’s extrinsic curvature.
• C. Gaussian curvature
  Gaussian curvature is a fundamental concept in differential geometry that measures how a surface bends at a point by combining its principal curvatures into a single intrinsic quantity.
• D. Gauss–Codazzi equations
  The Gauss–Codazzi equations are fundamental compatibility conditions in differential geometry that relate the intrinsic curvature of a surface to its extrinsic curvature as embedded in a higher-dimensional space.
• E. Theorema Egregium
  Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
• F. None of above. chosen