Geometry of solutions to the c-projective metrizability equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134121" target="_blank" >RIV/00216224:14310/23:00134121 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10231-022-01283-x" target="_blank" >https://doi.org/10.1007/s10231-022-01283-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10231-022-01283-x" target="_blank" >10.1007/s10231-022-01283-x</a>

Result language
angličtina
Original language name
Geometry of solutions to the c-projective metrizability equation
Original language description
On an almost complex manifold, a quasi-Kahler metric, with canonical connection in the c-projective class of a given minimal complex connection, is equivalent to a nondegenerate solution of the c-projectively invariant metrizability equation. For this overdetermined equa-tion, replacing this maximal rank condition on solutions with a nondegeneracy condition on the prolonged system yields a strictly wider class of solutions with non-vanishing (generalized) scalar curvature. We study the geometries induced by this class of solutions. For each solution, the strict point-wise signature partitions the underlying manifold into strata, in a manner that generalizes the model, a certain Lie group orbit decomposition of CPm. We describe the smooth nature and geometric structure of each strata component, generalizing the geometries of the embedded orbits in the model. This includes a quasi-Kahler metric on the open strata components that becomes singular at the strata boundary. The closed strata inherit almost CR-structures and can be viewed as a c-projective infinity for the given quasi-Kahler metric.
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
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-11473S" target="_blank" >GA20-11473S: Symmetry and invariance in analysis, geometric modelling and control theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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