Complex Manifold Deformation Theory 3 Uniqueness of Word

Complex Manifold Deformation Theory 

3 Uniqueness of Word

TANAKA Akio  

Conjecture

Word has uniqueness.

[Explanation]
1
Smooth manifold     M
Hermitian metric of M     h    
Tangent bundle of      T_M    
positive definite Hermitian inner product over T_M      h

Local coordinate system     z₁, ..., z_n 

Hermitian symmetric positive definite function's matrix     h_ij    

h = h_ijz_ij
Correspondence differential form     w

w = h_ijdzⁱd_j

When dw = 0, h is called Kller metric and w is called Kllerform.

Complex manifold that has Kller metric     Kller manifold

2

n-dimensional compact Kller manifold     X

Kller metric of X     g

Correspondence Kller form     w

Local coordinate system z₁, ..., z_n 

Ricci curvature of X     R = - log det (g)

Ricci form    Ric(w) = Rdzd

A certain constant     c

When Ric(w) = cw, g is called Kller-Einstein metric.

When c = 0, c₁(X) = 0

When c = -1, Linear bundle ⁿTX 's cobundle is ample. The situation is briefly abbreviate expressed by c₁(X) <0.

3

Compact Kller manifold     X

X satisfies c₁(X) = 0 or c₁(X) <0.
When Kller form's cohomology class is fixed, Kller-Einstein metric exists uniquely.

[Comment]

When word is expressed by compact Kller manifold in adequate condition, word has uniqueness.

[References]

Quantum Theory for Language Group / Sekinan Linguistic Field

Mirror Theory Group / Tokyo December 9, 2008 / Sekinan Linguistic Field

Especially the next is important.

Uniformity / Tokyo December 18, 2004 / Sekinan Linguistic Field

Fixation / Tokyo February 20, 2005 / Sekinan Linguistic Field

To be continued
Tokyo December 11, 2008
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