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A connection Γ is said to be the Ehresmann connection if, for each path x([0,1]) in X, there exists its horizontal lift through any point y ∈ π −1 (x([0,1])). A fibered manifold is a fiber bundle if and only if it admits such an Ehresmann connection.
Connections on a surface can be defined in a variety of ways. The Riemannian connection or Levi-Civita connection [9] is perhaps most easily understood in terms of lifting vector fields, considered as first order differential operators acting on functions on the manifold, to differential operators on sections of the frame bundle. In the case of ...
Cartan connections were quite rigidly tied to the underlying differential topology of the manifold because of their relationship with Cartan's equivalence method. Ehresmann connections were rather a solid framework for viewing the foundational work of other geometers of the time, such as Shiing-Shen Chern , who had already begun moving away ...
Manifold injection is a mixture formation system for internal combustion engines with external mixture formation. It is commonly used in engines with spark ignition that use petrol as fuel, such as the Otto engine, and the Wankel engine.
The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel.Levi-Civita, [1] along with Gregorio Ricci-Curbastro, used Christoffel's symbols [2] to define the notion of parallel transport and explore the relationship of parallel transport with the curvature, thus developing the modern notion of holonomy.
The flow in manifolds is extensively encountered in many industrial processes when it is necessary to distribute a large fluid stream into several parallel streams, or to collect them into one discharge stream, such as in fuel cells, heat exchangers, radial flow reactors, hydronics, fire protection, and irrigation. Manifolds can usually be ...
An inlet manifold or intake manifold (in American English) is the part of an internal combustion engine that supplies the fuel/air mixture to the cylinders. [1] The word manifold comes from the Old English word manigfeald (from the Anglo-Saxon manig [many] and feald [repeatedly]) and refers to the multiplying of one (pipe) into many.
An affine connection may also be defined as a principal GL(n) connection ω on the frame bundle FM or GL(M) of a manifold M. In more detail, ω is a smooth map from the tangent bundle T(F M ) of the frame bundle to the space of n × n matrices (which is the Lie algebra gl ( n ) of the Lie group GL( n ) of invertible n × n matrices) satisfying ...