1 Spacetime is putted to manifold.
2 When spacetime is expressed by sphere, spacetime becomes sphere symmetry.
Refer to the following paper.
Word Containing Time and 4 Dimensional Sphere Tokyo April 5, 2007
3 The symmetry is special orthogonal transformational group.
4 Generally n-dimensional SO(n) is compact Rie group.
5 On symmetry of spacetime, geometric invariant is presented.
Now on invariant, metric tensor g is presented.
g = Σgij dxidxj
g’s invariant transformation is isometry group.
When gij → gji is established, infinitesimal motion (Killing vector field) is 0.
6 Here Ricci flow is expressed by the following.
g(t) = gij(t)
∂gij / ∂t = -2Rij
Rij is Ricci curvature tensor.
7 M defined by a time interval [0, T] has a unique g(0) = go on Ricci flow.
8 (S4,g0) is 4 dimensional sphere surface with radius 1.
g(t) = r(t)2g0
g(t) has finite time T = 1/2(n-1).
Ricci flow becomes a point after finite time.
Phenomenon what manifold becomes smaller dimensional space is called collapse.
9 Now word has meaning and time.
10 Here word is expressed by manifold.
Refer to the following paper.
Topological Tolerance Tokyo Junr 7, 2006
Super Fluidity Tokyo June 17, 2006
Also refer to the following paper.
Structure of Word April 6, 2007
On time of language, refer to the following paper.
On Time Property Inherent in Charaters Hakuba March 28, 2003
On time principle of language, refer to the following paper.
Quantum Theory for Language Synopsis Tokyo January 15, 2004
10 Here time of word is defined by manifold’s time of Ricci flow’s collapse.
11 By Thurston conjecture, when compact 3 dimensional manifold is cut and separated by 2 dimensional sphere and torus, while generated compact manifold has sphere boundary, sphere is put together there. As the result new generated manifold has locally uniform structure.
Refer to the following paper.
Cut and Glue Cut-tube-ring generates multidimensional world Tokyo July 7, 2006
Also refer to the following paper.
Torus Chain Tokyo June 10, 2006
12 Peculiar solution of Thurston conjecture is Poincaré conjecture that is what simply connected 3 dimensional compact manifold is homomorphic to 3 dimensional sphere surface S3.
13 According by Thurston conjecture, what put together newly generated 3 dimensional manifold is called connected sum.
Connected sum is expressed by M1#M2. M1 and M2 are 3 dimensional manifolds.
14 Here sentence is defined by manifold’s connected sum.
Tokyo April 24, 2007
No comments:
Post a Comment