ON THE GEOMETRIC STRUCTURE OF CURRENTS TANGENT TO SMOOTH DISTRIBUTIONS br

被引：0

作者：

Alberti, Giovanni ^{[1
]}

Massaccesi, Annalisa ^{[2
]}

Stepanov, Eugene ^{[3
,4
]}

机构：

[1] Univ Pisalargo, Dipartimento Matemat, Largo Pontecorvo 5, I-56127 Pisa, Italy

[2] Univ Padua, Dipartimento Tecn & Gest Sistemi Ind DTG, Stradella S Nicola 3, I-36100 Vicenza, Italy

[3] Russian Acad Sci, Steklov Inst Math, St Petersburg Branch, Fontanka 27, St Petersburg 191023, Russia

[4] Higher Sch Econ, Fac Math, Usacheva 6, Moscow 119048, Russia

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2022年 / 122卷 / 01期

基金：

欧洲研究理事会; 俄罗斯基础研究基金会;

关键词：

SIZE;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known that a k-dimensional smooth surface in a Eu-clidean space cannot be tangent to a non-involutive distribution of k-dimensional planes. In this paper we discuss the extension of this statement to weaker notions of surfaces, namely integral and normal currents. We find out that integral currents behave to this regard exactly as smooth surfaces, while the behavior of normal currents is rather multifaceted. This issue is strictly related to a geometric property of the boundary of currents, which is also discussed in details.

引用

页码：1 / 33

页数：33

共 50 条

[1] Geometric representations of currents and distributions
Harrison, J
[J]. FRACTAL GEOMETRY AND STOCHASTICS III, 2004, 57 : 193 - 204
[2] GEOMETRIC ASPECTS OF CURRENTS AND DISTRIBUTIONS
EELLS, J
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1955, 41 (07) : 493 - 496
[3] A new geometric structure on tangent bundles
Georgiou, Nikos
Guilfoyle, Brendan
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2022, 172
[4] Geometric Anosov flows of dimension five with smooth distributions
Fang, Y
[J]. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2005, 4 (03) : 333 - 362
[5] On the tangent cones to plurisubharmonic currents
Dabbek, Khalifa
Ghiloufi, Noureddine
Hbil, Jawhar
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2016, 140 (05): : 562 - 574
[6] Differential and geometric structure for the tangent bundle of a projective limit manifold.
Galanis, GN
[J]. RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2004, 112 : 103 - 115
[7] Existence of tangent cones to plurisubharmonic currents
Haggui, Fathi
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2014, 59 (03) : 299 - 308
[8] Geometric structure in smooth dual and local Langlands conjecture
Aubert, Anne-Marie
Baum, Paul
Plymen, Roger
Solleveld, Maarten
[J]. JAPANESE JOURNAL OF MATHEMATICS, 2014, 9 (02): : 99 - 136
[9] Geometric structure in smooth dual and local Langlands conjecture
Anne-Marie Aubert
Paul Baum
Roger Plymen
Maarten Solleveld
[J]. Japanese Journal of Mathematics, 2014, 9 : 99 - 136
[10] AFFINE GEOMETRIC SPACES IN TANGENT CATEGORIES
Blute, R. F.
Cruttwell, G. S. H.
Lucyshyn-Wright, R. B. B.
[J]. THEORY AND APPLICATIONS OF CATEGORIES, 2019, 34 : 405 - 437

← 1 2 3 4 5 →