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user9072
user9072

weWe know that the Riemann tensor is antisymmetric with respect to the first two vectors ( thethe vectors that we parallel transport the third vector around the parallelogram made by their integral curves  ). But

But what is the geometric interpretation? whyWhy do we have to expect that by changing the order of parallel transportation we will have the same vector with opposite orientation?

we know that the Riemann tensor is antisymmetric with respect to the first two vectors ( the vectors that we parallel transport the third vector around the parallelogram made by their integral curves  ). But what is the geometric interpretation? why do we have to expect that by changing the order of parallel transportation we will have the same vector with opposite orientation?

We know that the Riemann tensor is antisymmetric with respect to the first two vectors (the vectors that we parallel transport the third vector around the parallelogram made by their integral curves).

But what is the geometric interpretation? Why do we have to expect that by changing the order of parallel transportation we will have the same vector with opposite orientation?

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DAVID
DAVID
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Interpretation of Riemann tensor antisymmetry

we know that the Riemann tensor is antisymmetric with respect to the first two vectors ( the vectors that we parallel transport the third vector around the parallelogram made by their integral curves ). But what is the geometric interpretation? why do we have to expect that by changing the order of parallel transportation we will have the same vector with opposite orientation?