| Title:
|
Cocalibrated $G_2$-manifolds with Ricci flat characteristic connection (English) |
| Author:
|
Friedrich, Thomas |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
21 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
1-13 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Any 7-dimensional cocalibrated $G_2$-manifold admits a unique connection $\nabla$ with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the $\nabla$-Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of $\nabla$-parallel vector fields. (English) |
| Keyword:
|
cocalibrated $G_2$-manifolds |
| Keyword:
|
connections with torsion |
| MSC:
|
53C25 |
| MSC:
|
81T30 |
| idZBL:
|
Zbl 06202721 |
| idMR:
|
MR3067118 |
| . |
| Date available:
|
2013-07-18T15:22:53Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143343 |
| . |
| Reference:
|
[1] Agricola, I., Ferreira, A.C.: Einstein manifolds with skew torsion.to appear. |
| Reference:
|
[2] Agricola, I., Friedrich, Th.: On the holonomy of connections with skew-symmetric torsion.Math. Ann., 328, 2004, 711-748, Zbl 1055.53031, MR 2047649, 10.1007/s00208-003-0507-9 |
| Reference:
|
[3] Agricola, I., Friedrich, Th.: The Casimir operator of a metric connection with skew-symmetric torsion.J. Geom. Phys., 50, 2004, 188-204, Zbl 1080.53043, MR 2078225, 10.1016/j.geomphys.2003.11.001 |
| Reference:
|
[4] Agricola, I., Friedrich, Th.: A note on flat connections with antisymmetric torsion.Diff. Geom. its Appl., 28, 2010, 480-487, MR 2651537, 10.1016/j.difgeo.2010.01.004 |
| Reference:
|
[5] Apostolov, V., Armstrong, J., Draghici, T.: Local rigidity of certain classes of almost Kähler 4-manifolds.Math. Ann., 323, 2002, 633-666, Zbl 1032.53016, MR 1921552, 10.1007/s002080200319 |
| Reference:
|
[6] Apostolov, V., Draghici, T., Moroianu, A.: A splitting theorem for Kähler manifolds whose Ricci tensors have constant eigenvalues.Internat. J. Math., 12, 2001, 769-789, Zbl 1111.53303, MR 1850671, 10.1142/S0129167X01001052 |
| Reference:
|
[7] Friedrich, Th.: G$_2$-manifolds with parallel characteristic torsion.J. Diff. Geom. Appl., 25, 2007, 632-648, Zbl 1141.53019, MR 2373939, 10.1016/j.difgeo.2007.06.010 |
| Reference:
|
[8] Friedrich, Th., Ivanov, S.: Parallel spinors and connections with skew-symmetric torsion in string theory.Asian J. Math., 6, 2002, 303-336, Zbl 1127.53304, MR 1928632 |
| Reference:
|
[9] Friedrich, Th., Ivanov, S.: Killing spinor equation in dimension 7 and geometry of integrable G$_2$-manifolds.J. Geom. Phys., 48, 2003, 1-11, MR 2006222, 10.1016/S0393-0440(03)00005-6 |
| Reference:
|
[10] Grantcharov, D., Grantcharov, G., Poon, Y.S.: Calabi-Yau connections with torsion on toric bundles.J. Differential Geom., 78, 2008, 13-32, Zbl 1171.53044, MR 2406264 |
| Reference:
|
[11] LeBrun, C.: Explicit self-dual metrics on CP2 # ... # CP2.J. Differential Geom., 34, 1991, 223-253, MR 1114461 |
| . |
