A geodesic is the shortest path between two points on a curved surface or in a curved space. In mathematics and physics, this concept is often applied in differential geometry and general relativity. - **In Geometry**: On a sphere, for example, geodesics are represented by great circles (like the equator or the lines of longitude).

A geodesic manifold is a type of manifold in differential geometry where the notion of distance and the concept of geodesics, which are the shortest paths between points, can be defined. More specifically, it often refers to a Riemannian manifold equipped with a Riemannian metric, allowing for the computation of distances and angles.

The Gibbons–Hawking ansatz is a concept in theoretical physics, particularly in the study of gravitational instantons, which are solutions to the classical equations of general relativity. Named after the physicists Gary Gibbons and Stephen Hawking, the ansatz constructs a specific form of metric that is useful for exploring the properties of four-dimensional manifolds, especially in the context of quantum gravity and the study of black hole thermodynamics.

In differential geometry and algebraic geometry, the concept of a **stable normal bundle** primarily arises in the context of vector bundles over a variety or a manifold. A normal bundle is associated with a submanifold embedded in a manifold.

A radio beacon is a device that transmits specific radio signals to provide information about its location or to assist in navigation. These signals can be used by ships, aircraft, and other vehicles to determine their position.

Jan Tauc is a notable figure known for his work in the fields of physics and materials science, particularly in the study of semiconductors and related materials. He has contributed to the understanding of optical and electrical properties of various materials.

The "Glossary of Riemannian and Metric Geometry" typically refers to a collection of terms and definitions commonly used in the fields of Riemannian geometry and metric geometry. These fields study the properties of spaces that are equipped with a notion of distance and curvature.

A glossary of differential geometry and topology typically includes key terms and concepts that are fundamental to these fields of mathematics. Here are some important terms that you might find in such a glossary: ### Differential Geometry 1. **Differentiable Manifold**: A topological manifold with a structure that allows for the differentiation of functions. 2. **Tangent Space**: The vector space consisting of the tangent vectors at a point on a manifold.

"Discoveries" by Joseph A. Dellinger is a literary work that explores themes of realization, understanding, and the process of uncovering truths in various contexts, whether personal, social, or scientific.

Jonathan Wahl could refer to several individuals depending on the context. If you're looking for a specific person, could you provide more details or specify the field he is associated with (e.g., arts, academia, business)? There are various individuals with that name, and more context would help narrow it down.

Gromov's inequality is a significant result in the field of differential geometry, particularly concerning the characteristics of complex projective spaces. It provides a lower bound for the volume of a k-dimensional holomorphic submanifold in a complex projective space in relation to the degree of the submanifold and the dimension of the projective space.

The Haefliger structure, often referred to in the context of differential geometry and topology, is a specific kind of manifold structure that arises in the study of pseudogroups and foliated spaces. It is named after André Haefliger, who contributed significantly to the classification of certain types of smooth structures on manifolds.

Hitchin's equations are a set of differential equations that arise in the context of mathematical physics, particularly in the study of stable connections and Higgs bundles on Riemann surfaces. They were introduced by Nigel Hitchin in the early 1990s and have connections to gauge theory, algebraic geometry, and string theory, among other fields.

The Heat Kernel Signature (HKS) is a mathematical and geometric concept used primarily in the field of shape analysis and computer graphics. It provides a way to describe and analyze the intrinsic properties of shapes, particularly in 3D geometry. The HKS is related to the heat diffusion process on a manifold; it's derived from the heat kernel, which describes how heat propagates through a space over time.

The Henneberg surface is a mathematical construct in the field of topology and geometric analysis. It is a type of non-orientable surface that can be described as a specific sort of 2-dimensional manifold. The surface is named after the mathematician Heinz Henneberg. One of the significant characteristics of the Henneberg surface is its unique structure.

A Hermitian Yang–Mills connection is a mathematical concept that arises in the field of differential geometry and gauge theory, particularly in the study of Yang–Mills theories and the geometry of complex manifolds. It is an important tool in areas such as algebraic geometry, gauge theory, and mathematical physics. ### Key Components: 1. **Hermitian Manifolds**: A Hermitian manifold is a complex manifold equipped with a Hermitian metric.

Joseph Bernstein could refer to several individuals, as it is a relatively common name. Without additional context, it's difficult to pinpoint exactly which Joseph Bernstein you are inquiring about. For example, there could be figures in academia, business, or other fields with that name.

A Hitchin system is a mathematical structure that arises in the study of integrable systems, particularly in the context of differential geometry and algebraic geometry. It is named after Nigel Hitchin, who introduced these systems in the context of the theory of stable bundles and the geometry of moduli spaces. More specifically, a Hitchin system is typically defined on a compact Riemann surface and can be understood as a certain type of symplectic manifold.

Holonomy is a concept from differential geometry and mathematical physics that describes the behavior of parallel transport around closed loops in a manifold. It provides insight into the geometric properties of the space, including curvature and how certain geometric structures behave under parallel transport.

Homological mirror symmetry (HMS) is a conjectural framework in mathematical physics and algebraic geometry that relates certain aspects of symplectic geometry and algebraic geometry. It emerges primarily from the work of Maxim Kontsevich in the late 1990s. The conjecture provides a deep relationship between the geometry of a space and the derived category of coherent sheaves on that space, particularly in the context of mirror symmetry—a phenomenon that originated in string theory.