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11-05-2005, 04:53 PM

Quote:
Originally Posted by AntonioLao
Spinors are two elements matrices. The twistors are 16 elements matrices.
Is there anything further from twistor theory, with more than 16 elements matrices?
  
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Einstein tensor
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Einstein tensor - 11-05-2005, 05:00 PM

Twistors have the same number of elements as Einstein tensor of general relativity.


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
  
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11-05-2005, 05:12 PM

Quote:
Originally Posted by AntonioLao
Twistors have the same number of elements as Einstein tensor of general relativity.
Do tensors have more elements in matrix form than twistors?
  
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other tensors can have more
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other tensors can have more - 11-05-2005, 05:18 PM

Quote:
Originally Posted by GUILLE
Do tensors have more elements in matrix form than twistors?
The answer is yes. But the Einstein tensor, the Riemann-Ricci tensor, the metric tensor of general relativity have the same number of elements as the twistor matrix, a 4 by 4 square matrix.


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
  
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11-05-2005, 05:23 PM

Quote:
Originally Posted by AntonioLao
The answer is yes. But the Einstein tensor, the Riemann-Ricci tensor, the metric tensor of general relativity have the same number of elements as the twistor matrix, a 4 by 4 square matrix.
Is the riemann-ricci tensor to do with the riemann hypothesis or the riemann zeta function, or the """"" integral, or the """"" manifolds, or the """"" mapping theorem, or the """""" surfaces, or the """""" sphere?
  
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Not related
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Not related - 11-05-2005, 05:29 PM

The Riemann tensor of general relativity is that of differential geometry. The other Riemanns are from number theory.


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
  
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11-05-2005, 05:36 PM

Quote:
Originally Posted by AntonioLao
The Riemann tensor of general relativity is that of differential geometry. The other Riemanns are from number theory.
Differential geometry, great, for it is one of the maths I'm making myself to learn this year. But it will be of the very last, for before it I need to understand what makes it up, and understand what makes up those which make it up.
  
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intrinsic curvature
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intrinsic curvature - 11-05-2005, 05:43 PM

differential geometry studies intrinsic (looking in) curvatures in contrast to extrinsic (looking out) curvatures.


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
  
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11-05-2005, 05:51 PM

Quote:
Originally Posted by AntonioLao
differential geometry studies intrinsic (looking in) curvatures in contrast to extrinsic (looking out) curvatures.
Let me guess: antiderivatives (or integrals) study extrinsic curvatures?
  
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not sure
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not sure - 11-05-2005, 05:57 PM

I need to look it up. I am not sure about the antiderivative part.


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
  
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