Lagrangian submanifolds in strict nearly Kähler 6-manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00506686" target="_blank" >RIV/67985840:_____/19:00506686 - isvavai.cz</a>

Výsledek na webu

<a href="https://projecteuclid.org/euclid.ojm/1563242426" target="_blank" >https://projecteuclid.org/euclid.ojm/1563242426</a>

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Lagrangian submanifolds in strict nearly Kähler 6-manifolds

Popis výsledku v původním jazyce

Lagrangian submanifolds in strict nearly Kähler 6-manifolds are related to special Lagrangian submanifolds in Calabi-Yau 6-manifolds and coassociative cones in G2-manifolds. We prove that the mean curvature of a Lagrangian submanifold L in a nearly Kähler manifold (M,J,g) is symplectically dual to the Maslov 1-form on L. Using relative calibrations, we derive a formula for the second variation of the volume of a Lagrangian submanifold L3 in a strict nearly Kähler manifold (M6,J,g) and compare it with McLean's formula for special Lagrangian submanifolds. We describe a finite dimensional local model of the moduli space of compact Lagrangian submanifolds in a strict nearly Kähler 6-manifold. We show that there is a real analytic atlas on (M6,J,g) in which the strict nearly Kähler structure (J,g) is real analytic. Furthermore, w.r.t. an analytic strict nearly Kähler structure the moduli space of Lagrangian submanifolds of M6 is a real analytic variety, whence infinitesimal Lagrangian deformations are smoothly obstructed if and only if they are formally obstructed. As an application, we relate our results to the description of Lagrangian submanifolds in the sphere S6 with the standard nearly Kähler structure described in [34].

Název v anglickém jazyce

Lagrangian submanifolds in strict nearly Kähler 6-manifolds

Popis výsledku anglicky

Lagrangian submanifolds in strict nearly Kähler 6-manifolds are related to special Lagrangian submanifolds in Calabi-Yau 6-manifolds and coassociative cones in G2-manifolds. We prove that the mean curvature of a Lagrangian submanifold L in a nearly Kähler manifold (M,J,g) is symplectically dual to the Maslov 1-form on L. Using relative calibrations, we derive a formula for the second variation of the volume of a Lagrangian submanifold L3 in a strict nearly Kähler manifold (M6,J,g) and compare it with McLean's formula for special Lagrangian submanifolds. We describe a finite dimensional local model of the moduli space of compact Lagrangian submanifolds in a strict nearly Kähler 6-manifold. We show that there is a real analytic atlas on (M6,J,g) in which the strict nearly Kähler structure (J,g) is real analytic. Furthermore, w.r.t. an analytic strict nearly Kähler structure the moduli space of Lagrangian submanifolds of M6 is a real analytic variety, whence infinitesimal Lagrangian deformations are smoothly obstructed if and only if they are formally obstructed. As an application, we relate our results to the description of Lagrangian submanifolds in the sphere S6 with the standard nearly Kähler structure described in [34].

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-00496S" target="_blank" >GA18-00496S: Singulární prostory ze speciální holonomie a foliací</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Osaka Journal of Mathematics

ISSN

0030-6126

e-ISSN

—

Svazek periodika

56

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

JP - Japonsko

Počet stran výsledku

29

Strana od-do

601-629

Kód UT WoS článku

000475677200009

EID výsledku v databázi Scopus

2-s2.0-85070079261