Geometry of solutions to the c-projective metrizability equation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Geometry of solutions to the c-projective metrizability equation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Geometry of solutions to the c-projective metrizability equation

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-11473S" target="_blank" >GA20-11473S: Symetrie a invariance v analýze, geometrickém modelování a teorii optimálního řízení</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annali di Matematica Pura ed Applicata

ISSN

0373-3114

e-ISSN

1618-1891

Svazek periodika

202

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

26

Strana od-do

1343-1368

Kód UT WoS článku

000899050100001

EID výsledku v databázi Scopus

2-s2.0-85143753206