Two-dimensional geodesic flows having first integrals of higher degree

Kazuyoshi Kiyohara

doi:10.1007/PL00004483

Two-dimensional geodesic flows having first integrals of higher degree

Kazuyoshi Kiyohara

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

We present a family of riemannian metrics on two-sphere having the property that the geodesic flows admit first integrals which are fiberwise homogeneous polynomials of degree greater than 2. They also have the property that all geodesics are closed.

Original language	English
Pages (from-to)	487-505
Number of pages	19
Journal	Mathematische Annalen
Volume	320
Issue number	3
DOIs	https://doi.org/10.1007/PL00004483
Publication status	Published - Jan 1 2001
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/PL00004483

Cite this

@article{4a2299c56efa4a358f6c50e5d1805c63,

title = "Two-dimensional geodesic flows having first integrals of higher degree",

abstract = "We present a family of riemannian metrics on two-sphere having the property that the geodesic flows admit first integrals which are fiberwise homogeneous polynomials of degree greater than 2. They also have the property that all geodesics are closed.",

author = "Kazuyoshi Kiyohara",

year = "2001",

month = jan,

day = "1",

doi = "10.1007/PL00004483",

language = "English",

volume = "320",

pages = "487--505",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Two-dimensional geodesic flows having first integrals of higher degree

AU - Kiyohara, Kazuyoshi

PY - 2001/1/1

Y1 - 2001/1/1

N2 - We present a family of riemannian metrics on two-sphere having the property that the geodesic flows admit first integrals which are fiberwise homogeneous polynomials of degree greater than 2. They also have the property that all geodesics are closed.

AB - We present a family of riemannian metrics on two-sphere having the property that the geodesic flows admit first integrals which are fiberwise homogeneous polynomials of degree greater than 2. They also have the property that all geodesics are closed.

UR - http://www.scopus.com/inward/record.url?scp=0035597679&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035597679&partnerID=8YFLogxK

U2 - 10.1007/PL00004483

DO - 10.1007/PL00004483

M3 - Article

AN - SCOPUS:0035597679

SN - 0025-5831

VL - 320

SP - 487

EP - 505

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3

ER -

Two-dimensional geodesic flows having first integrals of higher degree

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this