Open main menu

Diffgeom β


Torsion is tensorial

258 bytes added, 17:56, 6 January 2012
Then, <math>\tau(\nabla)</math> is a [[fact about::tensorial map]] in both coordinates. In other words, the value of <math>\tau(\nabla)</math> at a point <math>p \in M</math> depends only on <math>\nabla, X(p), Y(p)</math> and does not depend on the values of the vectors fields <math>X,Y</math> at points other than <math>p</math>.
More explicitly, for any point <math>p \in M</math>, <math>\tau(\nabla)</math> defines a bilinear map:
<math>\! \tau(\nabla): T_p(M) \times T_p(M) \to T_p(M)</math>
Further, since in fact [[torsion is antisymmetric]], this is an alternating bilinear map.
==Related facts==
Bureaucrats, emailconfirmed, Administrators