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@article{1730696,
author = {Gover, A. Rod and Neusser, Katharina and Willse, Travis},
article_location = {Warszawa},
article_number = {2019},
doi = {http://dx.doi.org/10.4064/dm786-7-2019},
keywords = {projective differential geometry; Sasaki-Einstein manifolds; holonomy reductions of Cartan connection; conformal geometry; special contact geometries; Kahler manifolds; CR geometry},
language = {eng},
issn = {0012-3862},
journal = {Dissertationes Mathematicae},
title = {Projective geometry of Sasaki-Einstein structures and their compactification},
url = {https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/online/113324/projective-geometry-of-sasaki-einstein-structures-and-their-compactification},
volume = {546},
year = {2019}
}
TY - JOUR
ID - 1730696
AU - Gover, A. Rod - Neusser, Katharina - Willse, Travis
PY - 2019
TI - Projective geometry of Sasaki-Einstein structures and their compactification
JF - Dissertationes Mathematicae
VL - 546
IS - 2019
SP - 1-64
EP - 1-64
PB - Institute of Mathematics. Polish Academy of Sciences
SN - 00123862
KW - projective differential geometry
KW - Sasaki-Einstein manifolds
KW - holonomy reductions of Cartan connection
KW - conformal geometry
KW - special contact geometries
KW - Kahler manifolds
KW - CR geometry
UR - https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/online/113324/projective-geometry-of-sasaki-einstein-structures-and-their-compactification
L2 - https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/online/113324/projective-geometry-of-sasaki-einstein-structures-and-their-compactification
N2 - We show that the standard definitions of Sasaki structures have elegant and simplifying interpretations in terms of projective differential geometry. For Sasaki-Einstein structures we use projective geometry to provide a resolution of such structures into geometrically less rigid components; the latter elemental components are separately, complex, orthogonal, and symplectic holonomy reductions of the canonical projective tractor/Cartan connection. This leads to a characterisation of Sasaki-Einstein structures as projective structures with certain unitary holonomy reductions. As an immediate application, this is used to describe the projective compactification of indefinite (suitably) complete noncompact Sasaki-Einstein structures and to prove that the boundary at infinity is a Fefferman conformal manifold that thus fibres over a nondegenerate CR manifold (of hypersurface type). We prove that this CR manifold coincides with the boundary at infinity for the c-projective compactification of the Kahler-Einstein manifold that arises, in the usual way, as a leaf space for the defining Killing field of the given Sasaki-Einstein manifold. A procedure for constructing examples is given. The discussion of symplectic holonomy reductions of projective structures leads us moreover to a new and simplifying approach to contact projective geometry. This is of independent interest and is treated in some detail.
ER -
GOVER, A. Rod, Katharina NEUSSER a Travis WILLSE. Projective geometry of Sasaki-Einstein structures and their compactification. \textit{Dissertationes Mathematicae}. Warszawa: Institute of Mathematics. Polish Academy of Sciences, 2019, roč.~546, č.~2019, s.~1-64. ISSN~0012-3862. Dostupné z: https://dx.doi.org/10.4064/dm786-7-2019.
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