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pro vyhledávání: '"Lafontaine, Jacques"'
Autor:
Mir, Chady El, Lafontaine, Jacques
We give a characterisation of Bieberbach manifolds which are geodesic boundaries of a compact flat manifold, and discuss the low dimensional cases, up to dimension 4.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/1710.02753
Autor:
Elmir, Chady, Lafontaine, Jacques
Publikováno v:
Annales de la facult\'e des sciences de Toulouse S\'er. 6, 22 no. 3 (2013), p. 623-648
A compact manifold is called Bieberbach if it carries a flat Riemannian metric. Bieberbach manifolds are aspherical, therefore the supremum of their systolic ratio, over the set of Riemannian metrics, is finite by a fundamental result of M. Gromov. W
Externí odkaz:
http://arxiv.org/abs/0912.3894
Autor:
Elmir, Chady, Lafontaine, Jacques
The systole of a compact non simply connected Riemannian manifold is the smallest length of a non-contractible closed curve ; the systolic ratio is the quotient $(\mathrm{systole})^n/\mathrm{volume}$. Its supremum on the set of all the riemannian met
Externí odkaz:
http://arxiv.org/abs/0804.1419
Akademický článek
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Autor:
Lafontaine, Jacques
K. Pankrashkin recently proved a nice geometric inequality. Namely , for any simple smooth curve enclosing a domain of area A, the maximum curvature k max satisfies k max ≥ π/A, and the equality holds if and only if the curve is a circle. In this
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::5c6e8b38fbaff8764a8716b4ddcf9b2e
https://hal.archives-ouvertes.fr/hal-01128887/file/ineg-aff.pdf
https://hal.archives-ouvertes.fr/hal-01128887/file/ineg-aff.pdf
Autor:
Lafontaine, Jacques
Publikováno v:
Introduction to Differential Manifolds; 2015, p349-395, 47p
Autor:
Lafontaine, Jacques
Publikováno v:
Introduction to Differential Manifolds; 2015, p323-348, 26p
Autor:
Lafontaine, Jacques
Publikováno v:
Introduction to Differential Manifolds; 2015, p273-321, 49p