Complex Manifold Deformation Theory Additional Paper 1 Map between Words

Complex Manifold Deformation Theory

Additional Paper

1 Map between Words

TANAKA Akio  

Conjecture

Words has map.

[View]
 (Theorem)
<line 1>Compact Riemann manifolds     (M, g), (N, h)
<line 2>Harmonic map from (M, g) to (N, h)      f
<line 3>Sectional curvature of (N, h)     everywhere non-positive
<line 4>If Ricci curvature of (M, g) is positive, f is constant map.
<line 5>If Ricci curvature of (M, g) is non-positive, f is all geodesic map.

[Impression]
1
Theorem is assumptively considered for words.
From <line 1>, words are assumed as compact Riemann manifolds.
From <line 2>, grammar is assumed as harmonic map.
From <line 3>, for instance, m-dimensional real hyperbolic type space has everywhere -1 sectional curvature.
From <line 4>, orthogonal frame field is considered.
Arbitrary point      xM
Neighborhood of x     U
Orthogonal frame field over U     {e_i}^m_i=1
 is constant over U d (e_i ) = 0
E() = 0
From <line 5>, geodesic is considered.
 is harmonic map ^M_'' = 0
2
Manifold that Ricci curvature of (M, g) is positive is defined as notional word.
Manifold that Ricci curvature of (M, g) is non-positive is defined as functional word.
On notional word and functional word, refer to the next.
#1 Quantification of Quantum / Tokyo May 21, 2004 / Sekinan Research Field of Language
Also refer to the next.
#2 Property of Quantum / Tokyo May 21, 2004 / Sekinan Research Field of Language

Tokyo January 5, 2009
Sekinan Research Field of language

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