**Applications**

Below are some examples of how differential geometry is applied to other fields of science and mathematics.

- In physics, three uses will be mentioned:
- Differential geometry is the language in which Einstein's general theory of relativity is expressed. According to the theory, the universe is a smooth manifold equipped with a pseudo-Riemannian metric, which describes the curvature of space-time. Understanding this curvature is essential for the positioning of satellites into orbit around the earth. Differential geometry is also indispensable in the study of gravitational lensing and black holes.
- Differential forms are used in the study of electromagnetism.
- Differential geometry has applications to both Lagrangian mechanics and Hamiltonian mechanics. Symplectic manifolds in particular can be used to study Hamiltonian systems.

- In economics, differential geometry has applications to the field of econometrics.
- Geometric modeling (including computer graphics) and computer-aided geometric design draw on ideas from differential geometry.
- In engineering, differential geometry can be applied to solve problems in digital signal processing.
- In probability, statistics, and information theory, one can interpret various structures as Riemannian manifolds, which yields the field of information geometry, particularly via the Fisher information metric.
- In structural geology, differential geometry is used to analyze and describe geologic structures.
- In computer vision, differential geometry is used to analyze shapes.
- In image processing, differential geometry is used to process and analyse data on non-flat surfaces.
- Grigori Perelman's proof of the PoincarĂ© conjecture using the techniques of Ricci flows demonstrated the power of the differential-geometric approach to questions in topology and it highlighted the important role played by its analytic methods.

Read more about this topic: Differential Geometry

### Other articles related to "applications, application":

X Servers - Limitations and Criticism - Network

... Screen in relation to terminals), and other

... Screen in relation to terminals), and other

**applications**and toolkits provide related facilities ... This ability allows the user interface (mouse, keyboard, monitor) of a running**application**to be switched from one location to another without stopping and restarting the**application**... This can be important in some**applications**, such as process monitoring and control ...Photoresist Categories -

... Microelectronics This

**Applications**... Microelectronics This

**application**, mainly applied to silicon wafers/silicon integrated circuits is the most developed of the technologies and the most specialized in the field ...Biotechnology -

... The first genetically modified food product was a tomato which was transformed to delay its ripening ... Researchers in Indonesia, Malaysia, Thailand, Philippines and Vietnam are currently working on delayed-ripening papaya in collaboration with the University of Nottingham and Zeneca ...

**Applications**- Agriculture - Improved Taste, Texture or Appearance of Food... The first genetically modified food product was a tomato which was transformed to delay its ripening ... Researchers in Indonesia, Malaysia, Thailand, Philippines and Vietnam are currently working on delayed-ripening papaya in collaboration with the University of Nottingham and Zeneca ...

Building On OpenStep

... was to use OpenStep code as a basis for network-wide

... was to use OpenStep code as a basis for network-wide

**applications**running across different platforms, as opposed to using CORBA or some other system ... which defined an operating system that**applications**would run in, under PDO the libraries were compiled into the**application**itself, creating a stand-alone "native"**application**for a ... of a considerable amount of supporting code (Objective-C and the libraries), PDO**applications**were nevertheless considerably smaller than similar CORBA solutions, typically about one-half to one-third the size ...Transistor - Comparison With Vacuum Tubes - Advantages

... that have allowed transistors to replace their vacuum tube predecessors in most

... that have allowed transistors to replace their vacuum tube predecessors in most

**applications**are Small size and minimal weight, allowing the development ... suitable for small, battery-powered**applications**... No warm-up period for cathode heaters required after power**application**...