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The notion of a differentiable manifold refines that of a manifold by requiring the functions that transform between charts to be differentiable. In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus.
In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. . According to the basic insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite direc
Recall that a topological manifold is a topological space which is locally homeomorphic to . Differentiable manifolds (also called smooth manifolds) generalize the notion of smoothness on in the following sense: a differentiable manifold is a topological manifold with a differentiable atlas, i.e. a collection of maps from open subsets of to the manifold which are used to "pull back" the ...
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 ...
Geometric analysis also includes global analysis, which concerns the study of differential equations on manifolds, and the relationship between differential equations and topology. The following is a partial list of major topics within geometric analysis: Gauge theory; Harmonic maps; Kähler–Einstein metrics; Mean curvature flow; Minimal ...
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