In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle T ∗ Q {\displaystyle T^{*}Q} of a manifold Q . {\displaystyle...

it is used as an alternative to canonical: Tautological bundle Tautological line bundle Tautological one-form Tautology (grammar), unnecessary repetition...

possesses a canonical one-form θ called the tautological one-form, discussed below. The exterior derivative of θ is a symplectic 2-form, out of which a non-degenerate...

} First fundamental form Gaussian curvature Gauss–Codazzi equations Shape operator Third fundamental form Tautological one-form Guggenheimer, Heinrich...

form is provided by the Brioschi formula. Metric tensor Second fundamental form Third fundamental form Tautological one-form First Fundamental Form —...

In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of k {\displaystyle...

abstract case, this is done with the rather abstract notion of the tautological one-form.) For a robotic arm consisting of numerous rigid linkages, the configuration...

cotangent bundle; i.e. given by forms). The tautological one-form is a special case of the more general solder form, which provides a (co-)frame field...

one form on M. The tautological one-form is a unique one-form on the frame bundle of E that corresponds to idE. Denoted by θ, it is a tensorial form of...

abstract setting, the Legendre transformation corresponds to the tautological one-form.[further explanation needed] The strategy behind the use of Legendre...