18/08/2015 22:09
Complex Manifold Deformation Theory
Conjecture A
3 Uniqueness of Word
TANAKA Akio
Conjecture
Word has uniqueness.
[Explanation]
1
Smooth manifold M
Hermitian metric of M h
Tangent bundle of TM positive definite Hermitian inner product over TM h
Local coordinate system z1, ..., zn
Hermitian symmetric positive definite function's matrix hij
h = hijzij
Correspondence differential form w
w = hijdzidj
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, ..., zn
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
Sekinan Research Field of language
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