Arthur Besse does not appear to be a widely recognized term, individual, or concept, as of my last update in October 2021. It's possible that it could refer to a private individual or a less known entity not widely covered in publicly available information.

The term "bundle metric" can refer to different concepts depending on the context in which it is used, but it is often associated with measuring the performance or effectiveness of a group of items or activities that are considered together as a "bundle." Here are a couple of contexts in which "bundle metric" might be relevant: 1. **E-commerce & Marketing**: In the context of e-commerce, "bundle metrics" may refer to the performance of product bundles that are sold together.

Cocurvature is a concept used in differential geometry and general relativity, particularly in the study of geometrical properties of manifolds. It is often related to the understanding of how a curvature of a surface or an entity behaves with respect to different directions. In general, curvature refers to the way a geometric object deviates from being flat.

In differential geometry, the concept of **development** refers to a way of representing a curved surface as if it were flat, allowing for the analysis of the intrinsic geometry of the surface in a more manageable way. The term often pertains to the idea of "developing" the surface onto a plane or some other surface. This is frequently used in the context of the study of curves and surfaces, particularly in the context of Riemannian geometry.

The double tangent bundle is a mathematical construction in differential geometry that generalizes the notion of tangent bundles. To understand the double tangent bundle, we first need to comprehend what a tangent bundle is. ### Tangent Bundle For a smooth manifold \( M \), the tangent bundle \( TM \) is a vector bundle that consists of all tangent vectors at every point on the manifold.

A Dupin hypersurface is a specific type of hypersurface in differential geometry characterized by certain properties of its principal curvatures. More formally, a hypersurface in a Riemannian manifold is called a Dupin hypersurface if its principal curvatures are constant along the principal curvature directions.

An elliptic complex is a concept in the field of mathematics, specifically within the areas of partial differential equations and the theory of elliptic operators. It relates to elliptic differential operators and the mathematical structures associated with them. ### Key Concepts: 1. **Elliptic Operators**: These are a class of differential operators that satisfy a certain condition (the ellipticity condition), which ensures the well-posedness of boundary value problems. An operator is elliptic if its principal symbol is invertible.

Equivariant differential forms are a specific type of differential forms that respect certain symmetries in a mathematical or physical context, particularly in the fields of differential geometry and algebraic topology. These forms are often associated with group actions on manifolds, where the structure of the manifold and the properties of the forms are invariant under the action of a group.

The Euler characteristic of an orbifold is a generalization of the concept of the Euler characteristic of a manifold, adapted to account for the singularities and local symmetries present in orbifolds. An orbifold can be thought of as a space that locally looks like a quotient of a Euclidean space by a finite group of symmetries.

Filling radius is a concept in the field of mathematics, particularly in metric spaces and topology. It is often associated with the properties of sets, particularly in the context of potential theory, geometric measure theory, or dynamical systems. The filling radius of a set can be thought of as a measure of how "thick" or "full" a set is.

In mathematics, particularly in the context of differential geometry and theoretical physics, a **gauge group** refers to a group of transformations that can be applied to a system without altering the physical observables of that system. The concept primarily appears in two key areas: gauge theory in physics and in the study of fiber bundles in mathematics. ### 1.

General covariant transformations are a key concept in the field of differential geometry and theoretical physics, particularly in the contexts of general relativity and other theories that utilize a geometric framework for describing physical phenomena. In essence, a general covariant transformation is a transformation that applies to fields and geometric objects defined on a manifold, allowing them to change in a way that is consistent with the structure of that manifold.

Hilbert's lemma, specifically referring to a result concerning sequences or series, typically pertains to the field of functional analysis and has implications in various areas of mathematics, particularly in the study of series and convergence.

Dr. Nim is a computer program that plays the game of Nim, a mathematical strategy game. In the game of Nim, players take turns removing objects from distinct piles. The goal is typically to be the player who removes the last object. The game has strategic elements based on binary number theory, and optimal strategies can be derived from it. Dr. Nim, as a project or program, was specifically developed to demonstrate computer strategies and algorithms in playing Nim optimally.

K-stability is a concept in algebraic geometry and complex geometry that relates to the stability of certain geometric objects, particularly projective varieties and Fano varieties, under the action of the automorphism group of these varieties. The notion arises in the context of the minimal model program and plays a significant role in understanding the geometry and deformation theory of varieties.

Debating is a structured form of dialogue where individuals or teams present arguments for or against a specific proposition or resolution. It is often conducted in a formal setting, such as competitions, educational environments, or public forums, and aims to explore different perspectives on an issue, enhance critical thinking, and improve public speaking skills. Key elements of debating include: 1. **Proposition (Resolution)**: The statement being argued.

Geoffrey Notkin is an American television personality, author, and entrepreneur known for his work in the fields of science, meteorite hunting, and adventure. He gained prominence as the host of the television series "Meteorite Men," which aired on the Science Channel and focused on his adventures in searching for meteorites around the world alongside his co-host, Steve Arnold.

Speakers' Corner is a designated public space in which individuals can freely express their opinions and ideas, often through speaking about political, social, or philosophical issues. The most famous Speakers' Corner is located in Hyde Park, London, where it has been a traditional site for free speech since the 19th century. At Speakers' Corner, anyone can step up and address an audience, attracting passersby who may wish to engage in discussion or debate.