Search results
Results from the WOW.Com Content Network
Introduction to Smooth Manifolds. Graduate Texts in Mathematics. Vol. 218 (Second ed.). New York London: Springer-Verlag. ISBN 978-1-4419-9981-8. OCLC 808682771. Introduction to Smooth Manifolds, Springer-Verlag, Graduate Texts in Mathematics, 2002, 2nd edition 2012 [6] Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds.
Important to applications in mathematics and physics [1] is the notion of a flow on a manifold. In particular, if M {\displaystyle M} is a smooth manifold and X {\displaystyle X} is a smooth vector field , one is interested in finding integral curves to X {\displaystyle X} .
Let be a smooth manifold; a (smooth) distribution assigns to any point a vector subspace in a smooth way. More precisely, consists of a collection {} of vector subspaces with the following property: Around any there exist a neighbourhood and a collection of vector fields, …, such that, for any point , span {(), …, ()} =.
For smooth manifolds M the problem reduces to finding the form of the homomorphism () (), where () is the oriented bordism group of X. [4] The connection between the bordism groups and the Thom spaces MSO(k) clarified the Steenrod problem by reducing it to the study of the homomorphisms ( ()) ().
Some constructions of smooth manifold theory, such as the existence of tangent bundles, [10] can be done in the topological setting with much more work, and others cannot. One of the main topics in differential topology is the study of special kinds of smooth mappings between manifolds, namely immersions and submersions , and the intersections ...
Let :, (,) be a (left) group action of a Lie group on a smooth manifold ; it is called a Lie group action (or smooth action) if the map is differentiable. Equivalently, a Lie group action of G {\displaystyle G} on M {\displaystyle M} consists of a Lie group homomorphism G → D i f f ( M ) {\displaystyle G\to \mathrm {Diff} (M)} .
In mathematics, at the junction of singularity theory and differential topology, Cerf theory is the study of families of smooth real-valued functions : on a smooth manifold, their generic singularities and the topology of the subspaces these singularities define, as subspaces of the function space.
In automotive engineering, an exhaust manifold collects the exhaust gases from multiple cylinders into one pipe. The word manifold comes from the Old English word manigfeald (from the Anglo-Saxon manig [many] and feald [fold]) [1] and refers to the folding together of multiple inputs and outputs (in contrast, an inlet or intake manifold ...