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In geometry, the notion of a connection makes precise the idea of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a parallel and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data one wants to transport.
This misconception, sometimes called the equal transit-time fallacy, is widespread among textbooks and non-technical reference books, and even appears in pilot training materials. In fact, the air moving over the top of an aerofoil generating lift is always moving much faster than the equal transit theory would imply, [ 448 ] as described in ...
In mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points.
A principal G-connection on a principal G-bundle over a smooth manifold is a particular type of connection that is compatible with the action of the group . A principal connection can be viewed as a special case of the notion of an Ehresmann connection , and is sometimes called a principal Ehresmann connection .
Popular mathematics is the act of presenting mathematics without technical terms. [208] Presenting mathematics may be hard since the general public suffers from mathematical anxiety and mathematical objects are highly abstract. [209] However, popular mathematics writing can overcome this by using applications or cultural links. [210]
In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. Viewed infinitesimally, a connection is a way of differentiating geometric data in such a manner that the derivative is also geometrically meaningful.
Get ready for all of the NYT 'Connections’ hints and answers for #220 on Wednesday, January 17, 2024. Connections game for Wednesday, January 17, 2024 The New York Times
the connection is torsion-free, i.e., T ∇ is zero, so that ∇ X Y − ∇ Y X = [X, Y]; parallel transport is an isometry, i.e., the inner products (defined using g) between tangent vectors are preserved. This connection is called the Levi-Civita connection. The term "symmetric" is often used instead of torsion-free for the first property.