Integrability versus topology of configuration manifolds and domains of possible motions

M Rudnev; VV Ten

Integrability versus topology of configuration manifolds and domains of possible motions

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Abstract

We establish a generic sufficient condition for a compact n-dimensional manifold bearing an integrable geodesic flow to be the n-torus. As a complementary result, we show that in the case of domains of possible motions with boundary, the first Betti number of the domain of possible motions may be arbitrarily large.

Translated title of the contribution	Integrability versus topology of configuration manifolds and domains of possible motions
Original language	English
Pages (from-to)	90 - 96
Journal	Archiv der Mathematik
Volume	86 (1)
Publication status	Published - Jan 2006

Bibliographical note

Publisher: Birkhauser Verlag AG
Other identifier: IDS Number: 014BS

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title = "Integrability versus topology of configuration manifolds and domains of possible motions",

abstract = "We establish a generic sufficient condition for a compact n-dimensional manifold bearing an integrable geodesic flow to be the n-torus. As a complementary result, we show that in the case of domains of possible motions with boundary, the first Betti number of the domain of possible motions may be arbitrarily large.",

author = "M Rudnev and VV Ten",

note = "Publisher: Birkhauser Verlag AG Other identifier: IDS Number: 014BS ",

year = "2006",

month = jan,

language = "English",

volume = "86 (1)",

pages = "90 -- 96",

journal = "Archiv der Mathematik",

issn = "1420-8938",

publisher = "Springer Verlag",

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TY - JOUR

T1 - Integrability versus topology of configuration manifolds and domains of possible motions

AU - Rudnev, M

AU - Ten, VV

N1 - Publisher: Birkhauser Verlag AG Other identifier: IDS Number: 014BS

PY - 2006/1

Y1 - 2006/1

N2 - We establish a generic sufficient condition for a compact n-dimensional manifold bearing an integrable geodesic flow to be the n-torus. As a complementary result, we show that in the case of domains of possible motions with boundary, the first Betti number of the domain of possible motions may be arbitrarily large.

AB - We establish a generic sufficient condition for a compact n-dimensional manifold bearing an integrable geodesic flow to be the n-torus. As a complementary result, we show that in the case of domains of possible motions with boundary, the first Betti number of the domain of possible motions may be arbitrarily large.

M3 - Article (Academic Journal)

SN - 1420-8938

VL - 86 (1)

SP - 90

EP - 96

JO - Archiv der Mathematik

JF - Archiv der Mathematik

ER -

Integrability versus topology of configuration manifolds and domains of possible motions

Abstract

Bibliographical note

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