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@article{2362443,
author = {Galaev, Anton},
article_location = {NEW YORK},
article_number = {2},
doi = {http://dx.doi.org/10.1007/s12220-018-0027-1},
keywords = {Lorentz-Kahler manifold; Holonomy group; Complex Walker coordinates; Complex pp-wave; Symmetric space; Space of oriented lines},
language = {eng},
issn = {1050-6926},
journal = {Journal of Geometric Analysis},
title = {Holonomy Classification of Lorentz-Kahler Manifolds},
volume = {29},
year = {2019}
}
TY - JOUR
ID - 2362443
AU - Galaev, Anton
PY - 2019
TI - Holonomy Classification of Lorentz-Kahler Manifolds
JF - Journal of Geometric Analysis
VL - 29
IS - 2
SP - 1075-1108
EP - 1075-1108
PB - Springer
SN - 10506926
KW - Lorentz-Kahler manifold
KW - Holonomy group
KW - Complex Walker coordinates
KW - Complex pp-wave
KW - Symmetric space
KW - Space of oriented lines
N2 - The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-Kahler manifolds are classified. A simple construction of a metric for each holonomy algebra is given. Complex Walker coordinates are introduced and described using the potential. Complex pp-waves are characterized in terms of the curvature, holonomy, and the potential. Classification of Lorentz-Kahler symmetric spaces is reviewed.
ER -
GALAEV, Anton. Holonomy Classification of Lorentz-Kahler Manifolds. \textit{Journal of Geometric Analysis}. NEW YORK: Springer, 2019, roč.~29, č.~2, s.~1075-1108. ISSN~1050-6926. Dostupné z: https://dx.doi.org/10.1007/s12220-018-0027-1.
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