By Luis Alvarez-Gaumé, Enrico Arbarello, Corrado De Concini, Nigel J. Hitchin (auth.), Mauro Francaviglia, Francesco Gherardelli (eds.)

**Read Online or Download Global Geometry and Mathematical Physics: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Montecatini Terme, Italy, July 4–12, 1988 PDF**

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**Additional resources for Global Geometry and Mathematical Physics: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Montecatini Terme, Italy, July 4–12, 1988**

**Example text**

Is t r i v i a l property action manifolds on - an SO(3) I~3. on w h i c h on the 3 - d i m e n s i o n a l There SO(3) space action by are two acts - those of c o v a r i a n t and those for w h i c h it is non-trival. In 29 this case ~3' we have a non-trivial the three K~hler with information computing enables can g = where a, are extra S0(3) rotates el' ~2 and k = 2, action is a 4 - d i m e n s i o n a l which rotates to circumvent in t h e the the difficult s t y l e of G r o i s s i e r which describes all hyperkMhler K~hler forms.

1) is the Fisher i n f o r m a t i o n coordinate-invariant. of m e a s u r e dx, since if dyi dx so ~f~_ d y i 2dx = ~Yi hf ~ fP: ~ 12 . matrix). It is a l s o fdx = fdx, indethen 23 Note also that since fMfdX f = 1 0 : IM and hence, [- yi j differentiating ~yi~y (log f ) d x so an a l t e r n a t i v e (and (log the most to t a k e the G a u s s i a n p(x;y,o) y 1 p This accessible) in because gets limit line the built I~ 5 is the o = 0 for space of in c o n f o r m a l of the c o n s t a n t Which metric The original other one u s e s , statistical problem hand h y p e r k'~hl er case.

Math. geometry Phys. 112 of the (1987) 663-689. [Ha] L. J. Hitchin, Proc~ space with P o n t r j a g i n index 1 on the of G l o b a l A n a l y s i s [H] of the & Diff. Geom. "The s e l f - d u a l i t y L o n d o n Math. Soc. 55 Sp(1) 4-sphere",Annals. (to appear). equations (1987), of on a R i e m a n n 59-126. J. Hitchin, A. Karlhede, U. L i n d s t r d n & M . R o c e k , " H y p e r k a h l e r metrics and supersymmetry", Commun. Math. Phys. 108 (1987) 535-589. [JT] A. H. Taubes, [K] K. Kodaira, [Ku] K.