Homogeneous 8-manifolds admitting invariant Spin(7)-structures

被引：2

作者：

Alekseevsky, Dmitri ^{[1
,2
]}

Chrysikos, Ioannis ^{[2
]}

Fino, Anna ^{[3
]}

Raffero, Alberto ^{[3
]}

机构：

[1] Inst Informat Transmiss Problems, B Karetny Per 19, Moscow 127051, Russia

[2] Univ Hradec Kralove, Fac Sci, Rokitanskeho 62, Hradec Kralove 50003, Czech Republic

[3] Univ Torino, Dipartimento Matemat G Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2020年 / 31卷 / 08期

关键词：

RIEMANNIAN-MANIFOLDS; PARALLEL SPINORS; EINSTEIN-METRICS; SPACES; CLASSIFICATION;

D O I：

10.1142/S0129167X20500603

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study compact, simply connected, homogeneous 8-manifolds admitting invariant Spin(7)-structures, classifying all canonical presentations G/H of such spaces, with G simply connected. For each presentation, we exhibit explicit examples of invariant Spin(7)-structures and we describe their type, according to Fernandez classification. Finally, we analyze the associated Spin(7)-connection with torsion.

引用

页数：33

共 35 条

[1] Alekseevksy D. V., 2019, CLASS QUANTUM GRAVIT, V36
[2] ALEKSEEVSKII DV, 1975, FUNCTIONAL ANAL APPL, V0009, P00005
[3] SPIN STRUCTURES ON COMPACT HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS
Alekseevsky, D. V.
Chrysikos, I.
[J]. TRANSFORMATION GROUPS, 2019, 24 (03) : 659 - 689
[4] [Anonymous], 2001, GLOBAL DIFFERENTIAL
[5] The Alekseevskii conjecture in low dimensions
Arroyo, Romina M.
Lafuente, Ramiro A.
[J]. MATHEMATISCHE ANNALEN, 2017, 367 (1-2) : 283 - 309
[6] Parallel spinors and holonomy groups on pseudo-Riemannian spin manifolds
Baum, H
Kath, I
[J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 1999, 17 (01) : 1 - 17
[7] Besse A. L., 1987, ERGEBNISSE MATH IHRE, DOI DOI 10.1007/978-3-540-74311-8
[8] Low-dimensional homogeneous Einstein manifolds
Böhm, C
Kerr, MM
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (04) : 1455 - 1468
[9] Böhm C, 2004, J DIFFER GEOM, V67, P79
[10] METRICS WITH EXCEPTIONAL HOLONOMY
BRYANT, RL
[J]. ANNALS OF MATHEMATICS, 1987, 126 (03) : 525 - 576

← 1 2 3 4 →