Two-dimensional geodesic flows having first integrals of higher degree

Research output: Contribution to journalArticle

22 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 languageEnglish
Pages (from-to)487-505
Number of pages19
JournalMathematische Annalen
Volume320
Issue number3
DOIs
Publication statusPublished - 2001
Externally publishedYes

Fingerprint

Geodesic Flow
First Integral
Homogeneous Polynomials
Riemannian Metric
Geodesic
Closed
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Two-dimensional geodesic flows having first integrals of higher degree. / Kiyohara, Kazuyoshi.

In: Mathematische Annalen, Vol. 320, No. 3, 2001, p. 487-505.

Research output: Contribution to journalArticle

@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",
doi = "10.1007/s002080100209",
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

Y1 - 2001

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/s002080100209

DO - 10.1007/s002080100209

M3 - Article

VL - 320

SP - 487

EP - 505

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 3

ER -