Abstract

We consider a (real or complex) analytic manifold M. Assuming that F is a ring of all analytic functions, full or truncated with respect to the local coordinates on M; we study the (m ≥ 2)-derivations of all involutive analytic distributions over F and their respective normalizers.

Highlights

  • Introduction and PreliminaryWe know several embedding theorems in differential geometry, some of them are of John F

  • Certain property on a smooth manifold cannot be true on M, for example the global representation of a smooth function germ theorem

  • We state that the considered Lie algebras have enough sections more than constant ones in the Lie algebra of all analytic vector fields

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Summary

Introduction and Preliminary

We know several embedding theorems in differential geometry, some of them are of John F. Certain property on a smooth manifold cannot be true on M, for example the global representation of a smooth function germ theorem Grabowski had this problem when he studied derivations of the real or complex analytic vector fields Lie algebra cf [5] and he used Stein manifolds to avoid technical difficulties in them. In the end, we discuss the Lie algebras of holomorphic vector fields, especially when the holomorphic manifold is not a Stein one, and Lie algebras of locally polynomial vector fields on an analytic manifold M Their m-derivations as well as their normalizers can be characterized by using some results of Randriambololondrantomalala [7]. J Generalized Lie Theory Appl S2: 002. doi:10.4172/1736-4337.S2-002

John Nash
We set the real analytic vector field
It is permit to use Theorem

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