Lagrangian submanifolds in strict nearly Kähler 6-manifolds

Result code in 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>

Result on the web

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

DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Lagrangian submanifolds in strict nearly Kähler 6-manifolds

Original language description

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].

Czech name

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Czech description

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Type

J_imp - 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/GA18-00496S" target="_blank" >GA18-00496S: Singular spaces from special holonomy and foliations</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

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

Name of the periodical

Osaka Journal of Mathematics

ISSN

0030-6126

e-ISSN

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Volume of the periodical

56

Issue of the periodical within the volume

3

Country of publishing house

JP - JAPAN

Number of pages

29

Pages from-to

601-629

UT code for WoS article

000475677200009

EID of the result in the Scopus database

2-s2.0-85070079261