In differential geometry, an Ehresmann connection (after the French mathematician Charles Ehresmann who first formalized this concept) is a version of the notion of a connection, which makes sense on any smooth fiber bundle. In particular, it does not rely on the possible vector bundle structure of the underlying fiber bundle, but nevertheless, linear connections may be viewed as a special case. Another important special case of Ehresmann connections are principal connections on principal bundles, which are required to be equivariant in the principal Lie group action.
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Ehresmannconnection (after the French mathematician Charles Ehresmann who first formalized this concept) is a version of the notion of a connection,...
introduction of the concepts of Ehresmannconnection and of jet bundles, and for his seminar on category theory. Ehresmann was born in Strasbourg (at the...
the connection, the marked points given by s always move under parallel transport. Yet another way to define a Cartan connection is with an Ehresmann connection...
model Klein geometry Ehresmannconnection, gives a manner for differentiating sections of a general fibre bundle Electrical connection, allows the flow of...
(Koszul or linear Ehresmann) connection on a vector bundle. Originally the term affine connection is short for an affine connection in the sense of Cartan...
is enough that the connection be equivariant under positive rescalings: it need not be linear. That is, (cf. Ehresmannconnection#Vector bundles and covariant...
{\mathfrak {g}}} , and P → B be a principal G-bundle. Let ω be an Ehresmannconnection on P (which is a g {\displaystyle {\mathfrak {g}}} -valued one-form...
a vector on M, and d denotes the pushforward. Ehresmannconnection Cartan connection Affine connection Curvature form Griffiths & Harris (1978), Wells...
an affine connection or covariant derivative (on tensors); the curvature form of an Ehresmannconnection: see Ehresmannconnection, connection (principal...
the Gauss–Manin connection constructed in a manner analogous to that in which the Ehresmannconnection generalizes the Koszul connection. The construction...
Einstein–Cartan theory connection (vector bundle) connection (principal bundle) Ehresmannconnection curvature curvature form holonomy, local holonomy...
language, an Ehresmannconnection) and formulating all rates of change in terms of the covariant derivative with respect to this connection. The gauge field...
vectors in much the same way as with a covariant derivative. An Ehresmann or Cartan connection supplies a lifting of curves from the manifold to the total...
Differential form – Expression that may be integrated over a region Ehresmannconnection – Differential geometry construct on fiber bundles Fréchet derivative –...
integrable. An Ehresmannconnection on E is a choice of a complementary subbundle HE to VE in TE, called the horizontal bundle of the connection. At each point...
essentially to Charles Ehresmann. However, it is different from, though related to, what is commonly called an Ehresmannconnection. It is also different...
linear connection on the tangent bundle of a manifold. In older literature, the term linear connection is occasionally used for an Ehresmannconnection or...
T(TM\setminus 0)=H(TM\setminus 0)\oplus V(TM\setminus 0)} be an Ehresmannconnection on the slit tangent bundle TM\0 and consider the mapping D : ( T...
and the triple (TE, p∗, TM) is a smooth vector bundle. The general Ehresmannconnection TE = HE ⊕ VE on a vector bundle (E, p, M) can be characterized in...
understanding of differential forms, Charles Ehresmann who introduced the theory of fibre bundles and Ehresmannconnections, and others. Of particular importance...
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