| Title:
|
Abelian complex structures on 6-dimensional compact nilmanifolds (English) |
| Author:
|
Cordero, Luis A. |
| Author:
|
Fernández, Marisa |
| Author:
|
Ugarte, Luis |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
215-229 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We classify the $6$-dimensional compact nilmanifolds that admit abelian complex structures, and for any such complex structure $J$ we describe the space of symplectic forms which are compatible with $J$. (English) |
| Keyword:
|
nilpotent Lie algebras |
| Keyword:
|
abelian complex structures |
| Keyword:
|
symplectic forms |
| MSC:
|
17B30 |
| MSC:
|
53C15 |
| MSC:
|
53C30 |
| MSC:
|
53D05 |
| idZBL:
|
Zbl 1078.53020 |
| idMR:
|
MR1922123 |
| . |
| Date available:
|
2009-01-08T19:21:18Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119315 |
| . |
| Reference:
|
[1] Barberis M.L., Dotti Miatello I.G., Miatello R.J.: On certain locally homogeneous Clifford manifolds.Ann. Glob. Anal. Geom. 13 (1995), 289-301. Zbl 0832.53039, MR 1344484 |
| Reference:
|
[2] Benson C., Gordon C.S.: Kähler and symplectic structures on nilmanifolds.Topology 27 (1988), 513-518. Zbl 0672.53036, MR 0976592 |
| Reference:
|
[3] Cordero L.A., Fernández M., Gray A.: Symplectic manifolds with no Kähler structure.Topology 25 (1986), 375-380. MR 0842431 |
| Reference:
|
[4] Cordero L.A., Fernández M., Gray A., Ugarte L.: Nilpotent complex structures on compact nilmanifolds.Rend. Circolo Mat. Palermo 49 suppl. (1997), 83-100. MR 1602971 |
| Reference:
|
[5] Cordero L.A., Fernández M., Gray A., Ugarte L.: Compact nilmanifolds with nilpotent complex structure: Dolbeault cohomology.Trans. Amer. Math. Soc. 352 (2000), 5405-5433. MR 1665327 |
| Reference:
|
[6] Cordero L.A., Fernández M., de León M.: Compact locally conformal Kähler nilmanifolds.Geom. Dedicata 21 (1986), 187-192. MR 0861196 |
| Reference:
|
[7] Cordero L.A., Fernández M., Ugarte L.: Lefschetz complex conditions for complex manifolds.preprint, 2001. MR 1935862 |
| Reference:
|
[8] Hasegawa K.: Minimal models of nilmanifolds.Proc. Amer. Math. Soc. 106 (1989), 65-71. Zbl 0691.53040, MR 0946638 |
| Reference:
|
[9] Magnin L.: Sur les algèbres de Lie nilpotentes de dimension $\leq 7$.J. Geom. Phys. 3 (1986), 119-144. MR 0855573 |
| Reference:
|
[10] Mal'cev A.I.: On a class of homogeneous spaces.Amer. Math. Soc. Transl., no. 39 (1951). MR 0039734 |
| Reference:
|
[11] Morosov V.: Classification of nilpotent Lie algebras of order $6$.Izv. Vyssh. Uchebn. Zaved. Mat. 4 (1958), 161-171. MR 0130326 |
| Reference:
|
[12] Nomizu K.: On the cohomology of compact homogeneous spaces of nilpotent Lie groups.Ann. of Math. 59 (1954), 531-538. Zbl 0058.02202, MR 0064057 |
| Reference:
|
[13] Salamon S.: Complex structures on nilpotent Lie algebras.J. Pure Appl. Algebra 157 (2001), 311-333. Zbl 1020.17006, MR 1812058 |
| Reference:
|
[14] Tralle A., Oprea J.: Symplectic manifolds with no Kähler structure.Lecture Notes in Math. 1661, Springer, 1997. Zbl 0891.53001, MR 1465676 |
| Reference:
|
[15] Wang H.C.: Complex parallisable manifolds.Proc. Amer. Math. Soc. 5 (1954), 771-776. MR 0074064 |
| . |
