On a generalized Calabi-Yau equation

Hongyu Wang[1]; Peng Zhu[2]

  • [1] Yangzhou University School of Mathematical Science Yangzhou, Jiangsu 225002 (P. R. China)
  • [2] School of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu 225002, (P. R. China)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 5, page 1595-1615
  • ISSN: 0373-0956

Abstract

top
Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed almost-Kähler manifolds, we extend to arbitrary dimension a non-existence result proved in complex dimension 2 .

How to cite

top

Wang, Hongyu, and Zhu, Peng. "On a generalized Calabi-Yau equation." Annales de l’institut Fourier 60.5 (2010): 1595-1615. <http://eudml.org/doc/116315>.

@article{Wang2010,
abstract = {Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed almost-Kähler manifolds, we extend to arbitrary dimension a non-existence result proved in complex dimension $2$.},
affiliation = {Yangzhou University School of Mathematical Science Yangzhou, Jiangsu 225002 (P. R. China); School of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu 225002, (P. R. China)},
author = {Wang, Hongyu, Zhu, Peng},
journal = {Annales de l’institut Fourier},
keywords = {Calabi-Yau equation; symplectic form; almost complex structure; Hermitian metric; Nijenhuis tensor; pseudo holomorphic function; pseudo-holomorphic function},
language = {eng},
number = {5},
pages = {1595-1615},
publisher = {Association des Annales de l’institut Fourier},
title = {On a generalized Calabi-Yau equation},
url = {http://eudml.org/doc/116315},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Wang, Hongyu
AU - Zhu, Peng
TI - On a generalized Calabi-Yau equation
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 5
SP - 1595
EP - 1615
AB - Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed almost-Kähler manifolds, we extend to arbitrary dimension a non-existence result proved in complex dimension $2$.
LA - eng
KW - Calabi-Yau equation; symplectic form; almost complex structure; Hermitian metric; Nijenhuis tensor; pseudo holomorphic function; pseudo-holomorphic function
UR - http://eudml.org/doc/116315
ER -

References

top
  1. M. Audin, P. Gauduchon, Symplectic and almost complex manifolds, 117 (1994), 41-76, in Holomorphic curves in symplectic geometry, Ed. by M. Audin and J. Lafontaine MR1274926
  2. E. Calabi, The space of Kähler metrics, 2 (1954), 206-207, in Proceeding of the International Congress of Mathematicians 
  3. P. Delanoë, Sur l’analogue presque-complexe de l’équation de Calabi-Yau, Osaka J. Math. 33 (1996), 829-846 Zbl0878.53030MR1435456
  4. S. K. Donaldson, Two forms on four manifolds and elliptic equations, in Inspired by S. S. Chern, (2006), 153-172, World Sci. Publ., Hackensack, NJ Zbl1140.58018MR2313334
  5. C. Ehresmann, P. Libermann, Sur les structures presque hermitiennes isotropes, C. R. Acad. Sci. Paris 232 (1951), 1281-1283 Zbl0042.15904MR40790
  6. P. Gauduchon, Hermitian connections and Dirac operators, Bull. Un. Mat. Ital. B 11 (no. 2, suppl.) (1997), 257-288 Zbl0876.53015MR1456265
  7. M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347 Zbl0592.53025MR809718
  8. D. McDuff, D. Salamon, Introduction to symplectic topology, (1998), Oxford University Press Zbl0844.58029MR1698616
  9. J. Moser, On the volume elements of a manifold, Trans. AMS 120 (1965), 286-294 Zbl0141.19407MR182927
  10. V. Tosatti, B. Weinkove, S. Y. Yau, Taming symplectic forms and the Calabi-Yau equation, Proc. London Math. Soc. 97 (2008), 401-424 Zbl1153.53054MR2439667
  11. H. Wang, P. Zhu, Calabi-Yau equation on closed symplectic 4-manifolds 
  12. B. Weinkove, The Calabi-Yau equation on almost Kähler four manifolds, J. Diff. Geom. 76 (2007), 317-349 Zbl1123.32015MR2330417
  13. H. Weyl, The Classical groups, 1 (1973), Princeton University Press Zbl1024.20502MR1488158
  14. S. T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, I, Comm. Pure Appl. Math. 31 (1978), 339-411 Zbl0369.53059MR480350
  15. P. Zhu, On almost Hermitian manifolds, (2008) Zbl1199.53050

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.