Differentisl geometry internal contraction

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SUMMARY

The discussion centers on the internal contraction in differential geometry, specifically the transformation of the relation (df:U)(dh:V)-(dh:V)(df:V) into U(fdh:v)-V(fdh:U)-fdh:[U,V]. The participants express confusion regarding the notation used, particularly the meaning of symbols such as ":", "f", "h", "U", and "V". The conversation highlights the need for clarity in mathematical expressions and the importance of understanding contraction notation, which is typically represented by symbols like \iota or \lrcorner.

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  • Understanding of differential geometry concepts
  • Familiarity with contraction notation in tensor calculus
  • Knowledge of vector fields and their operations
  • Basic proficiency in mathematical notation and symbols
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  • Research the properties of internal contraction in differential geometry
  • Study the notation and applications of contraction symbols like \iota and \lrcorner
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Mathematicians, physics students, and researchers in differential geometry seeking to deepen their understanding of internal contraction and related mathematical notations.

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Hi
I am struggling to see how the relation:
(df:U)(dh:V)-(dh:V)(df:V) (1)
can be rewritten as:
U(fdh:v)-V(fdh:U)-fdh:[U,V] (2)

I have tried expanding (1) out by making a scalar vector product of Udh:V but i don't think that is right and i am just not sure how best to proceed. It was annoyingly skipped over in class today, any help or suggestions would be appreciated.
 
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I am very unclear as to what you are asking. Perhaps you could clarify? What is f,h,U,V? What does your : mean? Typically, I have seen contraction denoted by \iota or \lrcorner, so I do not know how to read this.
 

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