Let H, K be a couple of vector fields of class C1 in an open set U ⊂ ℝN+m, ℳ be a N-dimensional C1 submanifold of U and define T: = { z∈ ℳ: H(z) , K(z) ∈ Tzℳ}. Then the obvious property If z0 ∈ ℳ is an interior point (relative to ℳ)of T then [H,K](z0)∈Tz0ℳ admits the following generalization: If z0 ∈ ℳ is a superdensity point (relative to ℳ)of T then [H,K](z0)∈Tz0ℳ. As a corollary we get very easily the following result of [7]: Let D be a C1 distribution of rank N on an open set U ⊂ ℝN+m and let ℳ be a N-dimensional C1 submanifold of U. If z0 ∈ ℳ is a superdensity point (relative to ℳ)of the tangency set { z∈ ℳ: Tzℳ= D(z) } then D is involutive at z0.

Good Behaviour of Lie Bracket at a Superdensity Point of the Tangency Set of a Submanifold With Respect to a Rank 2 Distribution / Delladio, S.. - In: ANALYSIS MATHEMATICA. - ISSN 0133-3852. - 47:1(2021), pp. 67-80. [10.1007/s10476-020-0063-5]

Good Behaviour of Lie Bracket at a Superdensity Point of the Tangency Set of a Submanifold With Respect to a Rank 2 Distribution

Delladio S.
2021

Abstract

Let H, K be a couple of vector fields of class C1 in an open set U ⊂ ℝN+m, ℳ be a N-dimensional C1 submanifold of U and define T: = { z∈ ℳ: H(z) , K(z) ∈ Tzℳ}. Then the obvious property If z0 ∈ ℳ is an interior point (relative to ℳ)of T then [H,K](z0)∈Tz0ℳ admits the following generalization: If z0 ∈ ℳ is a superdensity point (relative to ℳ)of T then [H,K](z0)∈Tz0ℳ. As a corollary we get very easily the following result of [7]: Let D be a C1 distribution of rank N on an open set U ⊂ ℝN+m and let ℳ be a N-dimensional C1 submanifold of U. If z0 ∈ ℳ is a superdensity point (relative to ℳ)of the tangency set { z∈ ℳ: Tzℳ= D(z) } then D is involutive at z0.
1
Delladio, S.
Good Behaviour of Lie Bracket at a Superdensity Point of the Tangency Set of a Submanifold With Respect to a Rank 2 Distribution / Delladio, S.. - In: ANALYSIS MATHEMATICA. - ISSN 0133-3852. - 47:1(2021), pp. 67-80. [10.1007/s10476-020-0063-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/295175
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