Cocalibrated -manifolds with Ricci flat characteristic connection
Communications in Mathematics (2013)
- Volume: 21, Issue: 1, page 1-13
- ISSN: 1804-1388
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topFriedrich, 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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- LeBrun, C., Explicit self-dual metrics on CP2 # ... # CP2, J. Differential Geom., 34, 1991, 223-253, (1991) MR1114461
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