Complex Manifold Deformation Theory 5 Time of Word

Complex Manifold Deformation Theory

5 Time of Word

TANAKA Akio  

Conjecture

Word has time.

[View^¶]
¶Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains and vigorous port towns at dawn. 
1
Kähler manifold     X
Kähler form     w
A certain constant     c
Cohomology class of w     2πc₁(X)
c₁(X)>0
Kähler metric     g
Real C^∞ function     f
∫_X (e^f- 1)wⁿ = 0
Ric(w) -w = f
2
Monge-Ampère equation
(Equation 1)

Use continuity method
(Equation 1-2)

Kähler form     w' = w +  f
Ric(w') = tw' + (1-t)w'
δ>0
I = {  }
3



 is differential over t.
Ding's functional     F_w

4
(Lemma)
There exists constant that is unrelated with t.
When u_tis the solution of equation 1-2, the next is satisfied.
F_w(u_t)C
5
Proper of Ding's functional is defined by the next.
 Arbitrary constant     K 
Point sequence of arbitrary P(X, w)_K     {u_i}

(Theorem)
When F_w is proper, there exists Kähler-Einstein metric.

[Impression^¶]
¶ Impression is developed from the view.
1
 If word is expressed by u , language is expressed by F_w and comprehension of human being is expressed by C, what language is totally comprehended by human being is guaranteed.
Refere to the next paper.
#Guarantee of Language
2
If language is expressed by being properly generated, distance of language is expressed by Kähler-Einstein metric and time of language is expressed by t, all the situation of language is basically expressed by (Equation1-2).
Refer to the next paper.
#Distance Theory
3
If inherent time of word is expressed by t's [δ, 1], dynamism of meaning minimum is mathematically formulated by Monge-Ampère equation.
Refer to the next papers.
#1<For inherent time>
On Time Property Inherent in Characters
#2<For meaningminimum>
From Cell to Manifold
#3<For meaning minimum's finiteness>
Amplitude of Meaning Minimum


Tokyo December 23, 2008
Sekinan Research Field of language

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