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Anchor


An anchor is the bundle map rho from a vector bundle A to the tangent bundle TB satisfying

1. [rho(X),rho(Y)]=rho([X,Y]) and

2. [X,phiY]=phi[X,Y]+(rho(X)·phi)Y,

where X and Y are smooth sections of A, phi is a smooth function of B, and the bracket is the "Jacobi-Lie bracket" of a vector field.


See also

Bundle, Lie Algebroid

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References

Weinstein, A. "Groupoids: Unifying Internal and External Symmetry." Not. Amer. Math. Soc. 43, 744-752, 1996.

Referenced on Wolfram|Alpha

Anchor

Cite this as:

Weisstein, Eric W. "Anchor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Anchor.html

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