Nondegenerate(2-form)
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(Difference between revisions)
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| - | A two form <m> omega </m> is '''nondegenerate''' over a Manifold <m> M</m> | + | A two form <m> omega </m> is '''nondegenerate''' over a Manifold <m> M</m> '''iff''' for all <m> m in M</m> and for all <m>v in T_m M </m> <m> (iota_m omega(v) = 0) right m = 0</m> |
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| + | In other words, <m> omega </m> is '''nondegenerate''' over a Manifold <m> M</m> '''iff''' <m> omega </m> only defines an alternating bilinear form which is identically zero for the origin, should the origin be part of the manifold. | ||
Current revision as of 16:56, 3 May 2006
A two form <m> omega </m> is nondegenerate over a Manifold <m> M</m> iff for all <m> m in M</m> and for all <m>v in T_m M </m> <m> (iota_m omega(v) = 0) right m = 0</m>
In other words, <m> omega </m> is nondegenerate over a Manifold <m> M</m> iff <m> omega </m> only defines an alternating bilinear form which is identically zero for the origin, should the origin be part of the manifold.
