Curvatures of measure-preserving diffeomorphism groups of non-orientable surfaces

被引：0

作者：

Khesin, Boris ^{[1
]}

Langoen, Rene ^{[2
]}

Markina, Irina ^{[2
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON, Canada

[2] Univ Bergen, Dept Math, Bergen, Norway

来源：

NONLINEARITY | 2025年 / 38卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

non-orientable manifold; diffeomorphism group; sectional curvature; Euler equation; infinite-dimensional Lie group; totally geodesic submanifold; DES GROUPES;

D O I：

10.1088/1361-6544/adc968

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study curvatures of the groups of measure-preserving diffeomorphisms of non-orientable compact surfaces. For the cases of the Klein bottle and the real projective plane we compute curvatures, their asymptotics and the normalised Ricci curvatures in many directions. Extending the approach of Arnold and Lukatskii we provide estimates of weather unpredictability for natural models of trade wind currents on the Klein bottle and the projective plane.

引用

页数：38

共 16 条

[1] GEOMETRY OF A GROUP OF AREA-PRESERVING DIFFEOMORPHISMS
ARAKELYAN, TA
SAVVIDY, GK
[J]. PHYSICS LETTERS B, 1989, 223 (01) : 41 - 46
[2] SUR LA GEOMETRIE DIFFERENTIELLE DES GROUPES DE LIE DE DIMENSION INFINIE ET SES APPLICATIONS A LHYDRODYNAMIQUE DES FLUIDES PARFAITS
ARNOLD, V
[J]. ANNALES DE L INSTITUT FOURIER, 1966, 16 (01) : 319 - &
[3] ARNOLD V, 1965, CR HEBD ACAD SCI, V260, P5668
[4] Arnold V., 2021, Applied Mathematical Sciences, Vvol 125
[5] Arnold V.I., 1989, Mathematical Methods of Classical Mechanics, V60, DOI DOI 10.1007/978-1-4757-2063-1
[6] Balabanova NA, 2022, Arxiv, DOI arXiv:2202.06160
[7] Quantizing models of (2+1)-dimensional gravity on non-orientable manifolds
Chen, Si
Witt, Donald M.
Plotkin, Steven S.
[J]. CLASSICAL AND QUANTUM GRAVITY, 2014, 31 (05)
[8] Izosimov A., 2025, J. Symplectic Geom, V23
[9] Lee JM., 2013, INTRO SMOOTH MANIFOL, V218, DOI 10.1007/978-1-4419-9982-5
[10] Axisymmetric Diffeomorphisms and Ideal Fluids on Riemannian 3-Manifolds
Lichtenfelz, Leandro
Misiolek, Gerard
Preston, Stephen C.
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (01) : 446 - 485

← 1 2 →