scholarly journals The natural operators lifting projectable vector fields to some fiber product preserving bundles

2003 ◽  
Vol 81 (3) ◽  
pp. 261-271 ◽  
Author(s):  
W. M. Mikulski
Keyword(s):  
Vector Fields ◽  
Fiber Product ◽  
Natural Operators ◽  
Projectable Vector

ON SOME NATURAL OPERATORS IN VECTOR FIELDS

2003 ◽  
Vol 36 (1) ◽  
Author(s):  
Włodzimierz M. Mikulski
Keyword(s):  
Vector Fields ◽  
Natural Operators

scholarly journals Natural Operators Lifting Vector Fields to Bundles of Weil Contact Elements

2004 ◽  
Vol 54 (4) ◽  
pp. 855-867 ◽  
Author(s):  
Miroslav Kureš ◽  
Włodzimierz M. Mikulski
Keyword(s):  
Vector Fields ◽  
Natural Operators

scholarly journals The natural operators similar to the twisted courant bracket on couples of vector fields and p-forms

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4071-4078
Author(s):  
Włodzimierz Mikulski
Keyword(s):  
Vector Fields ◽  
Jacobi Identity ◽  
Natural Numbers ◽  
Normalization Condition ◽  
Courant Bracket ◽  
Natural Operator ◽  
Bilinear Operators ◽  
Natural Operators

Given natural numbers m and p with m ? p + 2 ? 3, all Mfm-natural operators A sending closed (p+2)-forms H on m-manifolds M into R-bilinear operators AH transforming pairs of couples of vector fields and p-forms on M into couples of vector fields and p-forms on M are found. If m ? p + 2 ? 3, all Mfm-natural operators A (as above) such that AH satisfies the Jacobi identity in Leibniz form are extracted, and that the twisted Courant bracket [-,-]H is the unique Mfm-natural operator AH (as above) satisfying the Jacobi identity in Leibniz form and some normalization condition is deduced.

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