Projective geometry of Sasaki-Einstein structures and their compactification
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00114700" target="_blank" >RIV/00216224:14310/19:00114700 - isvavai.cz</a>
Result on the web
<a href="https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/online/113324/projective-geometry-of-sasaki-einstein-structures-and-their-compactification" target="_blank" >https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/online/113324/projective-geometry-of-sasaki-einstein-structures-and-their-compactification</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/dm786-7-2019" target="_blank" >10.4064/dm786-7-2019</a>
Alternative languages
Result language
angličtina
Original language name
Projective geometry of Sasaki-Einstein structures and their compactification
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Dissertationes Mathematicae
ISSN
0012-3862
e-ISSN
1730-6310
Volume of the periodical
546
Issue of the periodical within the volume
2019
Country of publishing house
PL - POLAND
Number of pages
64
Pages from-to
1-64
UT code for WoS article
000559966700001
EID of the result in the Scopus database
2-s2.0-85078587080