Holography of Higher Codimension Submanifolds: Riemannian and
Conformal

J 2025

Holography of Higher Codimension Submanifolds: Riemannian and Conformal

BLITZ, Samuel Harris a Josef ŠILHAN

Základní údaje

Originální název

Holography of Higher Codimension Submanifolds: Riemannian and Conformal

Autoři

BLITZ, Samuel Harris (840 Spojené státy, domácí) a Josef ŠILHAN (203 Česká republika, domácí)

Vydání

Symmetry, Integrability and Geometry: Methods and Applications, KYIV 4, Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine, 2025, 1815-0659

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Ukrajina

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.900 v roce 2023

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.3842/SIGMA.2025.002

UT WoS

001389887200001

EID Scopus

2-s2.0-85215127638

Klíčová slova anglicky

Riemannian geometry; conformal geometry; submanifold embeddings; holo- graphy

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 27. 1. 2025 07:48, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal bundle. Qualitatively new behavior is observed in the higher-co dimension case, giving rise to new invariants that obstruct the order-by-order construction of unit defining maps. In the conformal setting, a novel invariant (that vanishes in co dimension 1) is realized as the leading transverse- order term appearing in a holographically-constructed Willmore invariant. Using these same tools, we also investigate the formal solutions to extension problems off of an embedded submanifold.

Návaznosti

EH22_010/0007541, projekt VaV

Název: MSCAfellow6_MUNI

GA22-00091S, projekt VaV

Název: Geometrické struktury, invariance a diferenciální rovnice se vztahem k matematické fyzice (Akronym: GSIDRVMF)

Investor: Grantová agentura ČR, Geometrické struktury, invariance a diferenciální rovnice se vztahem k matematické fyzice

Citovat

BLITZ, Samuel Harris a Josef ŠILHAN. Holography of Higher Codimension Submanifolds: Riemannian and Conformal. Symmetry, Integrability and Geometry: Methods and Applications. KYIV 4: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine, 2025, roč. 21, January, s. 1-41. ISSN 1815-0659. Dostupné z: https://dx.doi.org/10.3842/SIGMA.2025.002.

@article{2470142,
   author = {Blitz, Samuel Harris and Šilhan, Josef},
   article_location = {KYIV 4},
   article_number = {January},
   doi = {http://dx.doi.org/10.3842/SIGMA.2025.002},
   keywords = {Riemannian geometry; conformal geometry; submanifold embeddings; holo- graphy},
   language = {eng},
   issn = {1815-0659},
   journal = {Symmetry, Integrability and Geometry: Methods and Applications},
   title = {Holography of Higher Codimension Submanifolds: Riemannian and Conformal},
   url = {https://www.emis.de/journals/SIGMA/2025/002/},
   volume = {21},
   year = {2025}
}

TY  - JOUR
ID  - 2470142
AU  - Blitz, Samuel Harris - Šilhan, Josef
PY  - 2025
TI  - Holography of Higher Codimension Submanifolds: Riemannian and Conformal
JF  - Symmetry, Integrability and Geometry: Methods and Applications
VL  - 21
IS  - January
SP  - 1-41
EP  - 1-41
PB  - Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
SN  - 18150659
KW  - Riemannian geometry
KW  - conformal geometry
KW  - submanifold embeddings
KW  - holo- graphy
UR  - https://www.emis.de/journals/SIGMA/2025/002/
N2  - We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal bundle. Qualitatively new behavior is observed in the higher-co dimension case, giving rise to new invariants that obstruct the order-by-order construction of unit defining maps. In the conformal setting, a novel invariant (that vanishes in co dimension 1) is realized as the leading transverse- order term appearing in a holographically-constructed Willmore invariant. Using these same tools, we also investigate the formal solutions to extension problems off of an embedded submanifold.
ER  -

BLITZ, Samuel Harris a Josef ŠILHAN. Holography of Higher Codimension Submanifolds: Riemannian and Conformal. \textit{Symmetry, Integrability and Geometry: Methods and Applications}. KYIV 4: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine, 2025, roč.~21, January, s.~1-41. ISSN~1815-0659. Dostupné z: https://dx.doi.org/10.3842/SIGMA.2025.002.

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