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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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