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A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
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<div style="color:#00000a;">[01:11:22] It turns out. That if this is $$X^4$$</div> | <div style="color:#00000a;">[01:11:22] It turns out. That if this is $$X^4$$</div> | ||
<div style="color:#00000a;">[01:11:29] and this is this particular indogenous choice of $$U^14$$ we have a 10 dimensional metric along the fibers. So we have a $$G^{10}_{\mu nu}. Further for every point in the fibers, we get a metric downstairs on the base space. So if we pull back the cotangent bundle,</div> | <div style="color:#00000a;">[01:11:29] and this is this particular indogenous choice of $$U^14$$ we have a 10 dimensional metric along the fibers. So we have a $$G^{10}_{\mu nu}$$. Further for every point in the fibers, we get a metric downstairs on the base space. So if we pull back the cotangent bundle,</div> | ||
<div style="color:#00000a;">[01:11:59] we get a metric $$G^4_{\mu \nu} on $$\Pi^*$$ star of the cotangent bundle of X. We now define the chimeric bundle, right? And the chimeric bundle. Is this direct, some of the vertical tangent bundle along the fibers with the pullback, which we're going to call the horizontal bundle from the base space. So the chimeric bundle</div> | <div style="color:#00000a;">[01:11:59] we get a metric $$G^4_{\mu \nu}$$ on $$\Pi^*$$ star of the cotangent bundle of X. We now define the chimeric bundle, right? And the chimeric bundle. Is this direct, some of the vertical tangent bundle along the fibers with the pullback, which we're going to call the horizontal bundle from the base space. So the chimeric bundle</div> | ||
<div style="color:#00000a;">[01:12:33] is going to be the vertical tangent space of 10 dimensions to U direct sum, the four dimensional cotangent space which we're going to call horizontal to U. And the great thing about the chimeric bundle is, is that it has an a priori metric. It's got a metric on the four a metric on the 10 and we can always decide that the two of them are naturally perpendicular to each other.</div> | <div style="color:#00000a;">[01:12:33] is going to be the vertical tangent space of 10 dimensions to U direct sum, the four dimensional cotangent space which we're going to call horizontal to U. And the great thing about the chimeric bundle is, is that it has an a priori metric. It's got a metric on the four a metric on the 10 and we can always decide that the two of them are naturally perpendicular to each other.</div> | ||