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@article{1471622,
author = {Chrysikos, Ioannis and Gustad, Christian and Winther, Henrik},
article_location = {Amsterdam},
article_number = {April},
doi = {http://dx.doi.org/10.1016/j.geomphys.2018.10.012},
keywords = {Homogeneous space; Connection; Symmetric space; Irreducible; Isotropy},
language = {eng},
issn = {0393-0440},
journal = {Journal of Geometry and Physics},
title = {Invariant connections and Nabla-Einstein structures on isotropy irreducible spaces},
url = {https://doi.org/10.1016/j.geomphys.2018.10.012},
volume = {138},
year = {2019}
}
TY - JOUR
ID - 1471622
AU - Chrysikos, Ioannis - Gustad, Christian - Winther, Henrik
PY - 2019
TI - Invariant connections and Nabla-Einstein structures on isotropy irreducible spaces
JF - Journal of Geometry and Physics
VL - 138
IS - April
SP - 257-284
EP - 257-284
PB - Elsevier Science BV
SN - 03930440
KW - Homogeneous space
KW - Connection
KW - Symmetric space
KW - Irreducible
KW - Isotropy
UR - https://doi.org/10.1016/j.geomphys.2018.10.012
L2 - https://doi.org/10.1016/j.geomphys.2018.10.012
N2 - This paper is devoted to a systematic study and classification of invariant affine or metric connections on certain classes of naturally reductive spaces. For any non-symmetric, effective, strongly isotropy irreducible2homogeneous Riemannian manifold , we compute the dimensions of the spaces of -invariant affine and metric connections. For such manifolds we also describe the space of invariant metric connections with skew-torsion. For the compact Lie group we classify all bi-invariant metric connections, by introducing a new family of bi-invariant connections whose torsion is of vectorial type. Next we present applications related with the notion of -Einstein manifolds with skew-torsion. In particular, we classify all such invariant structures on any non-symmetric strongly isotropy irreducible homogeneous space.
ER -
CHRYSIKOS, Ioannis, Christian GUSTAD a Henrik WINTHER. Invariant connections and Nabla-Einstein structures on isotropy irreducible spaces. \textit{Journal of Geometry and Physics}. Amsterdam: Elsevier Science BV, roč.~138, April, s.~257-284. ISSN~0393-0440. doi:10.1016/j.geomphys.2018.10.012. 2019.
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