On Angles between Linear Subspaces in $\mathbb R^4$ and the Singularity
Matematičeskie zametki, Tome 115 (2024) no. 3, pp. 450-457 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We generalize the Khinchin singularity phenomenon for the problem in which, for a given irrational linear subspace, rational subspaces forming the least angle with the given subspace are sought.
Keywords: function of the measure of irrationality, singularity, angle between subspaces.
@article{MZM_2024_115_3_a10,
     author = {A. O. Chebotarenko},
     title = {On {Angles} between {Linear} {Subspaces} in $\mathbb R^4$ and the {Singularity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {450--457},
     year = {2024},
     volume = {115},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_115_3_a10/}
}
TY  - JOUR
AU  - A. O. Chebotarenko
TI  - On Angles between Linear Subspaces in $\mathbb R^4$ and the Singularity
JO  - Matematičeskie zametki
PY  - 2024
SP  - 450
EP  - 457
VL  - 115
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_2024_115_3_a10/
LA  - ru
ID  - MZM_2024_115_3_a10
ER  - 
%0 Journal Article
%A A. O. Chebotarenko
%T On Angles between Linear Subspaces in $\mathbb R^4$ and the Singularity
%J Matematičeskie zametki
%D 2024
%P 450-457
%V 115
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_2024_115_3_a10/
%G ru
%F MZM_2024_115_3_a10
A. O. Chebotarenko. On Angles between Linear Subspaces in $\mathbb R^4$ and the Singularity. Matematičeskie zametki, Tome 115 (2024) no. 3, pp. 450-457. http://geodesic.mathdoc.fr/item/MZM_2024_115_3_a10/

[1] A. Ya. Khintchine, “Über eine Klasse linearer diophantischer Approximationen”, Rendiconti Circ. Math. Palermo, 50:2 (1926), 170–195 | DOI

[2] V. Jarník, “Eine Bemerkung über diophantische Approximationen”, Math. Z., 72:1 (1959), 187–191 | DOI | MR

[3] J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge Univ. Press, New York, 1957 | MR

[4] N. G. Moschevitin, “Singulyarnye diofantovy sistemy A. Ya. Khinchina i ikh primenenie”, UMN, 65:3 (393) (2010), 43–126 | DOI | MR | Zbl

[5] D. Kleinbock, N. Moshchevitin, D. Weiss, “Singular vectors on manifolds and fractals”, Israel J. Math., 245:2 (2021), 589–613 | DOI | MR

[6] O. N. German, “Geometriya diofantovykh eksponent”, UMN, 78:2 (470) (2023), 71–148 | DOI | MR

[7] W. M. Schmidt, “On heights of algebraic subspaces and diophantine approximations”, Ann. of Math. (2), 85 (1967), 430–472 | DOI | MR

[8] E. Joseph, “On the approximation exponents for subspaces of $\mathbb{R}^n$”, Mosc. J. Comb. Number Theory, 11:1 (2022), 21-35 | DOI | MR

[9] N. Moshchevitin, “Über die Winkel zwischen Unterräumen”, Colloq. Math., 162:1 (2020), 143–157 | DOI | MR

[10] N. de Saxcé, Approximation Diophantienne sur la Grassmannienne, Preprint, 2022

[11] V. Khodzh, D. Pido, Metody algebraicheskoi geometrii, v. 1, IL, M., 1954 | MR