A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
Revision as of 03:50, 11 April 2020
, 11 April 2020→Choosing All Metrics
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<p>[01:11:22] It turns out if this is $$X^4$$ and this is this particular endogenous choice of $$U^{14}$$, we have a 10-dimensional metric along the fibers. So we have a $$g^{10}_{\mu\nu}$$. | <p>[01:11:22] It turns out if this is $$X^4$$ and this is this particular endogenous choice of $$U^{14}$$, we have a 10-dimensional metric along the fibers. So we have a $$g^{10}_{\mu\nu}$$. | ||
Further for every point in the fibers, we get a metric downstairs on the base space. So if we pull back the cotangent bundle, we get a metric $$g^4_{\mu\nu}$$ on $$\Pi^*$$ of the cotangent bundle of $$X$$. | Further, for every point in the fibers, we get a metric downstairs on the base space. So if we pull back the cotangent bundle, we get a metric $$g^4_{\mu\nu}$$ on $$\Pi^*$$ of the cotangent bundle of $$X$$. | ||
<p>[01:12:17] We now define the chimeric bundle, right? And the chimeric bundle is this direct sum of the vertical tangent bundle along the fibers with the pullback, which we're going to call the horizontal bundle from the base space. | <p>[01:12:17] We now define the chimeric bundle, right? And the chimeric bundle is this direct sum of the vertical tangent bundle along the fibers with the pullback, which we're going to call the horizontal bundle from the base space. | ||