The integral manifolds of these distributions are totally geodesic submanifolds.
2.
Thus the maximal integral manifold of ? is ( an open set of ) " M " itself.
3.
In 1945, Bogolyubov proved a fundamental theorem on the existence and basic properties of a one-parameter integral manifold for a system of non-linear differential equations.
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He investigated periodic and quasi-periodic solutions lying on a one-dimensional manifold, thus forming the foundation for a new method of non-linear mechanics, the " method of integral manifolds ".
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This is a contact structure, for the fiber of UT " M " is obviously an integral manifold ( the vertical bundle is everywhere in the kernel of ? ), and the remaining tangent directions are filled out by moving up the fiber of UT " M ".
6.
A Pfaffian system is said to be "'completely integrable "'if M admits a foliation by maximal integral manifolds . ( Note that the foliation need not be "'regular "'; i . e . the leaves of the foliation might not be embedded submanifolds .)
7.
This all-new TRD supercharger is compatible on all 2005 through 2015 model year Toyota Tacoma trucks, and 2007 through 2009 model year FJ Cruiser SUV . This supercharger system features Eaton roots-type rotating components in a one-piece integral manifold, iridium spark plugs, and a five-rib serpentine drive belt system.
8.
Given a collection of differential 1-forms \ textstyle \ alpha _ i, i = 1, 2, \ dots, k on an \ textstyle n-dimensional manifold M, an "'integral manifold "'is a submanifold whose tangent space at every point \ textstyle p \ in M is annihilated by each \ textstyle \ alpha _ i.
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