local Nagano theorem
Theorem (Local Nagano Theorem).
Let be an open neighbourhood of a point . Further let be a Lie subalgebra of the Lie algebra of real analytic real vector fields on which is also a -module. Then there exists a real analytic submanifold with , such that for all we have
Furthermore the germ of at is the unique germ of a submanifold with this property.
The union of all connected real analytic embedded submanifolds of whose germ at coincides with the germ of at is called the global Nagano leaf.
The global Nagano leaf turns out to be a connected immersed real analytic submanifold which may however not be an embedded submanifold of .
- 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
|Title||local Nagano theorem|
|Date of creation||2013-03-22 14:48:27|
|Last modified on||2013-03-22 14:48:27|
|Last modified by||jirka (4157)|
|Defines||local Nagano leaf|
|Defines||global Nagano leaf|