Cocalibrated G 2 -manifolds with Ricci flat characteristic connection

Thomas Friedrich

Communications in Mathematics (2013)

  • Volume: 21, Issue: 1, page 1-13
  • ISSN: 1804-1388

Abstract

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Any 7-dimensional cocalibrated G 2 -manifold admits a unique connection ∇ with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the ∇ -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of ∇ -parallel vector fields.

How to cite

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Friedrich, Thomas. "Cocalibrated $G_2$-manifolds with Ricci flat characteristic connection." Communications in Mathematics 21.1 (2013): 1-13. <http://eudml.org/doc/260720>.

@article{Friedrich2013,
abstract = {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.},
author = {Friedrich, Thomas},
journal = {Communications in Mathematics},
keywords = {cocalibrated $G_2$-manifolds; connections with torsion; cocalibrated -manifolds; connections with torsion; parallel vector fields},
language = {eng},
number = {1},
pages = {1-13},
publisher = {University of Ostrava},
title = {Cocalibrated $G_2$-manifolds with Ricci flat characteristic connection},
url = {http://eudml.org/doc/260720},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Friedrich, Thomas
TI - Cocalibrated $G_2$-manifolds with Ricci flat characteristic connection
JO - Communications in Mathematics
PY - 2013
PB - University of Ostrava
VL - 21
IS - 1
SP - 1
EP - 13
AB - 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.
LA - eng
KW - cocalibrated $G_2$-manifolds; connections with torsion; cocalibrated -manifolds; connections with torsion; parallel vector fields
UR - http://eudml.org/doc/260720
ER -

References

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  1. Agricola, I., Ferreira, A.C., Einstein manifolds with skew torsion, to appear. 
  2. Agricola, I., Friedrich, Th., 10.1007/s00208-003-0507-9, Math. Ann., 328, 2004, 711-748, (2004) Zbl1055.53031MR2047649DOI10.1007/s00208-003-0507-9
  3. Agricola, I., Friedrich, Th., 10.1016/j.geomphys.2003.11.001, J. Geom. Phys., 50, 2004, 188-204, (2004) Zbl1080.53043MR2078225DOI10.1016/j.geomphys.2003.11.001
  4. Agricola, I., Friedrich, Th., 10.1016/j.difgeo.2010.01.004, Diff. Geom. its Appl., 28, 2010, 480-487, (2010) MR2651537DOI10.1016/j.difgeo.2010.01.004
  5. Apostolov, V., Armstrong, J., Draghici, T., 10.1007/s002080200319, Math. Ann., 323, 2002, 633-666, (2002) Zbl1032.53016MR1921552DOI10.1007/s002080200319
  6. Apostolov, V., Draghici, T., Moroianu, A., 10.1142/S0129167X01001052, Internat. J. Math., 12, 2001, 769-789, (2001) Zbl1111.53303MR1850671DOI10.1142/S0129167X01001052
  7. Friedrich, Th., 10.1016/j.difgeo.2007.06.010, J. Diff. Geom. Appl., 25, 2007, 632-648, (2007) Zbl1141.53019MR2373939DOI10.1016/j.difgeo.2007.06.010
  8. Friedrich, Th., Ivanov, S., Parallel spinors and connections with skew-symmetric torsion in string theory, Asian J. Math., 6, 2002, 303-336, (2002) Zbl1127.53304MR1928632
  9. Friedrich, Th., Ivanov, S., 10.1016/S0393-0440(03)00005-6, J. Geom. Phys., 48, 2003, 1-11, (2003) MR2006222DOI10.1016/S0393-0440(03)00005-6
  10. Grantcharov, D., Grantcharov, G., Poon, Y.S., Calabi-Yau connections with torsion on toric bundles, J. Differential Geom., 78, 2008, 13-32, (2008) Zbl1171.53044MR2406264
  11. LeBrun, C., Explicit self-dual metrics on CP2 # ... # CP2, J. Differential Geom., 34, 1991, 223-253, (1991) MR1114461

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