Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Gauss–Codazzi equations | Statement: [Weingarten map, appearsIn, Gauss–Codazzi equations]

Target entity: Gauss–Codazzi equations
Context triple: [Weingarten map, appearsIn, Gauss–Codazzi equations]

• A. 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.
• B. Gauss–Bonnet theorem (early form)
  The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
• 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. Cartan structure equations
  Cartan structure equations are fundamental differential geometric relations that express curvature and torsion in terms of connection 1-forms on a manifold.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Gauss–Codazzi equations
Triple: [Weingarten map, appearsIn, 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.

Target entity: Gauss–Codazzi equations
Target entity description: 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.

• A. 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.
• B. Gauss–Bonnet theorem (early form)
  The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
• 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. Cartan structure equations
  Cartan structure equations are fundamental differential geometric relations that express curvature and torsion in terms of connection 1-forms on a manifold.
• E. 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.
• F. None of above. chosen