Compactifications of indefinite 3-Sasaki structures and their quaternionic Kähler quotients

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139365" target="_blank" >RIV/00216224:14310/24:00139365 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s10231-023-01385-0" target="_blank" >https://link.springer.com/article/10.1007/s10231-023-01385-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10231-023-01385-0" target="_blank" >10.1007/s10231-023-01385-0</a>

Result language
angličtina
Original language name
Compactifications of indefinite 3-Sasaki structures and their quaternionic Kähler quotients
Original language description
We show that 3-Sasaki structures admit a natural description in terms of projective differential geometry. First we establish that a 3-Sasaki structure may be understood as a projective structure whose tractor connection admits a holonomy reduction, satisfying a particular non-vanishing condition, to the (possibly indefinite) unitary quaternionic group Sp(p, q). Moreover, we show that, if a holonomy reduction to Sp(p, q) of the tractor connection of a projective structure does not satisfy this condition, then it decomposes the underlying manifold into a disjoint union of strata including open manifolds with (indefinite) 3-Sasaki structures and a closed separating hypersurface at infinity with respect to the 3-Sasaki metrics. It is shown that the latter hypersurface inherits a Biquard–Fefferman conformal structure, which thus (locally) fibers over a quaternionic contact structure, and which in turn compactifies the natural quaternionic Kähler quotients of the 3-Sasaki structures on the open manifolds. As an application, we describe the projective compactification of (suitably) complete, non-compact (indefinite) 3-Sasaki manifolds and recover Biquard’s notion of asymptotically hyperbolic quaternionic Kähler metrics.
Czech name
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Czech description
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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

Project
<a href="/en/project/GA19-06357S" target="_blank" >GA19-06357S: Geometric structures, differential operators and symmetries</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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