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: Riemannian geometry | Statement: [Optimal Transport: Old and New, subject, Riemannian geometry]

Target entity: Riemannian geometry
Context triple: [Optimal Transport: Old and New, subject, Riemannian geometry]

• A. Riemannian manifolds
  Riemannian manifolds are smooth manifolds equipped with an inner product on each tangent space that allows one to measure lengths, angles, and curvature in a curved geometric setting.
• B. differential geometry chosen
  Differential geometry is a branch of mathematics that uses the techniques of calculus and linear algebra to study the properties and curvature of smooth shapes and spaces such as curves, surfaces, and manifolds.
• C. Kähler geometry
  Kähler geometry is a branch of differential geometry studying complex manifolds equipped with a compatible symplectic form and Riemannian metric, leading to rich interactions between complex, symplectic, and Riemannian geometry.
• D. Ricci flow
  Ricci flow is a geometric evolution equation that smoothly deforms the metric of a Riemannian manifold in a way analogous to heat diffusion, playing a central role in Grigori Perelman's proof of the Poincaré conjecture.
• E. Lezioni di geometria differenziale
  Lezioni di geometria differenziale is a foundational textbook on differential geometry by Italian mathematician Luigi Bianchi, influential in the development of modern geometric theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.