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Volumn 62, Issue 3-4, 2003, Pages 247-276

The Riemannian geometry of orbit spaces - The metric, geodesics, and integrable systems

Author keywords

Geodesics; Invariants; Orbit spaces; Representations

Indexed keywords


EID: 0038585093     PISSN: 00333883     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (46)

References (38)
  • 2
    • 0001799360 scopus 로고
    • Über eine Verallgemeinerung der Riemann'schen Geometrie
    • A. D. ALEKSANDROV, Über eine Verallgemeinerung der Riemann'schen Geometrie, Schr. Forschungsinst. Math 1 (1957), 33-84.
    • (1957) Schr. Forschungsinst. Math , vol.1 , pp. 33-84
    • Aleksandrov, A.D.1
  • 5
    • 0010049449 scopus 로고
    • Engl. transl.
    • J. AVAN, O. BABELON and M. TALON, Construction of the classical R-matrices for the Toda and Calogero models jour Algebra i Analiz, Vol. 6, 1994, 67-89; Engl. transl.: St. Petersburg Math. J. 6, (1995), 255-274.
    • (1995) St. Petersburg Math. J. , vol.6 , pp. 255-274
  • 6
    • 0040645450 scopus 로고    scopus 로고
    • The symplectic structure of the spin Calogero model
    • arXiv:q-alg/9707011
    • O. BABELON and M. TALON, The symplectic structure of the spin Calogero model, Phys. Lett. A 236, 5-6 (1997), 462-468, arXiv:q-alg/9707011.
    • (1997) Phys. Lett. A , vol.236 , pp. 5-6
    • Babelon, O.1    Talon, M.2
  • 7
    • 0000303324 scopus 로고
    • Lifting cisotopies from orbit spaces
    • E. BIERSTONE, Lifting isotopies from orbit spaces, Topology 14 (1975), 245-252.
    • (1975) Topology , vol.14 , pp. 245-252
    • Bierstone, E.1
  • 8
    • 0007247539 scopus 로고
    • Orbifolds of maximal diameter
    • JOSEPH E. BORZELLINO, Orbifolds of maximal diameter, Indiana Univ. Math. J. 42 (1993), 37-53.
    • (1993) Indiana Univ. Math. J. , vol.42 , pp. 37-53
    • Borzellino, J.E.1
  • 9
    • 0038107822 scopus 로고    scopus 로고
    • The closed geodesic problem for compact Riemannian 2-orbifolds
    • JOSEPH E. BORZELLINO and BENJAMIN G. LORICA, The closed geodesic problem for compact Riemannian 2-orbifolds, Pac. J. Math. 175 (1996), 39-46.
    • (1996) Pac. J. Math. , vol.175 , pp. 39-46
    • Borzellino, J.E.1    Lorica, B.G.2
  • 10
    • 33646864986 scopus 로고
    • A. D. Alexandrov spaces with curvature bounded below
    • YU. BURAGO, M. GROMOV and G. PEREL'MAN, A. D. Alexandrov spaces with curvature bounded below, Russ. Math. Surv. 47 (1992), 1-58.
    • (1992) Russ. Math. Surv. , vol.47 , pp. 1-58
    • Burago, Yu.1    Gromov, M.2    Perel'man, G.3
  • 11
    • 0038784763 scopus 로고
    • Spectral geometry of V-manifolds and its application to harmonic maps
    • Differential geometry, Part 1: Partial differential equations on manifolds
    • YUAN-JEN CHIANG, Spectral geometry of V-manifolds and its application to harmonic maps, in: Differential geometry, Part 1: Partial differential equations on manifolds, Proc. Symp. Pure Math. 54, Part 1, 1993, 93-99.
    • (1993) Proc. Symp. Pure Math. , vol.54 , Issue.PART 1 , pp. 93-99
    • Chiang, Y.-J.1
  • 12
    • 0000055463 scopus 로고
    • Polar coordinates induced by actions of compact Lie groups
    • J. DADOK, Polar coordinates induced by actions of compact Lie groups, TAMS 288 (1985), 125-137.
    • (1985) TAMS , vol.288 , pp. 125-137
    • Dadok, J.1
  • 13
    • 0004076870 scopus 로고    scopus 로고
    • Metric Structures for Riemannian and Non-Riemannian Spaces
    • Birkhäuser, Boston, Basel, Berlin
    • M. GROMOV, Metric Structures for Riemannian and Non-Riemannian Spaces, Progress in Mathematics 152, Birkhäuser, Boston, Basel, Berlin, 1999.
    • (1999) Progress in Mathematics , vol.152
    • Gromov, M.1
  • 14
    • 84972556273 scopus 로고
    • Stable bundles and integrable systems
    • N. HITCHIN, Stable bundles and integrable systems, Duke Math. J. 54 (1987), 91-114.
    • (1987) Duke Math. J. , vol.54 , pp. 91-114
    • Hitchin, N.1
  • 15
    • 84980148563 scopus 로고
    • Hamiltonian group actions and dynamical systems of Calogero type
    • D. KAZHDAN, B. KOSTANT and S. STERNBERG, Hamiltonian group actions and dynamical systems of Calogero type, Comm. Pure Appl. Math. 31 (1978), 481-501.
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 481-501
    • Kazhdan, D.1    Kostant, B.2    Sternberg, S.3
  • 16
    • 0001775106 scopus 로고
    • Spin generalization of the Calogero-Moser system and the matrix KP equation
    • Topics in topology and mathematical physics, Amer, Amer. Math. Soc., Providence, arXiv:hep-th/9411160
    • I. M. KRICHEVER O. BABELON, E. BILEY and M. TALON, Spin generalization of the Calogero-Moser system and the matrix KP equation, in: Topics in topology and mathematical physics, Amer. Math. Soc. Transl. Ser. 2, 170, Amer. Math. Soc., Providence, 1995, 83-119, arXiv:hep-th/9411160.
    • (1995) Math. Soc. Transl. Ser. 2 , vol.170 , pp. 83-119
    • Krichever, I.M.1    Babelon, O.2    Biley, E.3    Talon, M.4
  • 17
    • 85159527924 scopus 로고    scopus 로고
    • Tensor fields and connections on holomorphic orbit spaces of finite groups
    • arXiv:math.DG/0203079 (to appear)
    • ANDREAS KRIEGL, MARK LOSIK and PETER W. MICHOR, Tensor fields and connections on holomorphic orbit spaces of finite groups, J. Lie Theory, arXiv:math.DG/0203079 (to appear).
    • J. Lie Theory
    • Kriegl, A.1    Losik, M.2    Michor, P.W.3
  • 18
    • 0000388063 scopus 로고
    • Examples of singular reduction
    • Symplectic geometry, Cambridge Univ. Press, Cambridge, 95h:58054
    • E. LERMAN, R. MONTGOMERY and R. SJAMAAR, Examples of singular reduction, in: Symplectic geometry, London Math. Soc. Lecture Note Ser., 192, Cambridge Univ. Press, Cambridge, 1993, 127-155, 95h:58054.
    • (1993) London Math. Soc. Lecture Note Ser. , vol.192 , pp. 127-155
    • Lerman, E.1    Montgomery, R.2    Sjamaar, R.3
  • 20
    • 0038447116 scopus 로고    scopus 로고
    • Lifts of diffeomorphisms of orbit spaces for representations of compact Lie groups
    • M. V. LOSIK, Lifts of diffeomorphisms of orbit spaces for representations of compact Lie groups, Geom. Dedicata 88 (2001), 21-36.
    • (2001) Geom. Dedicata , vol.88 , pp. 21-36
    • Losik, M.V.1
  • 22
    • 0002706826 scopus 로고
    • Stratifications and mappings
    • New York, Academic Press
    • J. N. MATHER, Stratifications and mappings, in: Dynamical systems, New York, Academic Press, 1973, 195-232.
    • (1973) Dynamical Systems , pp. 195-232
    • Mather, J.N.1
  • 23
    • 0000170683 scopus 로고
    • Differentiable invariants
    • J. N. MATHER, Differentiable invariants, Topology 16 (1977), 145-155.
    • (1977) Topology , vol.16 , pp. 145-155
    • Mather, J.N.1
  • 24
    • 29144469997 scopus 로고    scopus 로고
    • Isometric actions of Lie groups and invariants
    • PETER W. MICHOR, Isometric actions of Lie groups and invariants, Lecture course at the University of Vienna, 1996/97, http://www.mat.univie.ac.at/̃michor/tgbook.ps.
    • (1996) Lecture Course at the University of Vienna
    • Michor, P.W.1
  • 26
    • 34347230069 scopus 로고
    • Three integrable Hamiltonian systems connected with isospectral deformations
    • J. MOSER, Three integrable Hamiltonian systems connected with isospectral deformations, Adv. Math. 16 (1975), 197-220.
    • (1975) Adv. Math. , vol.16 , pp. 197-220
    • Moser, J.1
  • 27
    • 30444458560 scopus 로고
    • Geodesic flows on symmetric spaces of zero curvature and explicit solution of the generalized Calogero model for the classical case
    • M. OLSHANETSKII and A. PERELOMOV, Geodesic flows on symmetric spaces of zero curvature and explicit solution of the generalized Calogero model for the classical case, Funct. Anal. Appl. 10, 3 (1977), 237-239.
    • (1977) Funct. Anal. Appl. , vol.10 , Issue.3 , pp. 237-239
    • Olshanetskii, M.1    Perelomov, A.2
  • 28
    • 0011546968 scopus 로고
    • Classical integrable finite-dimensional systems related to Lie algebras
    • M. OLSHANETSKII and A. PERELOMOV, Classical integrable finite-dimensional systems related to Lie algebras, Phys. Rep. 71 (1981), 313-400.
    • (1981) Phys. Rep. , vol.71 , pp. 313-400
    • Olshanetskii, M.1    Perelomov, A.2
  • 29
    • 0001441560 scopus 로고
    • On the existence of slices for actions of non-compact Lie groups
    • PALAIS, R., On the existence of slices for actions of non-compact Lie groups, Ann. of Math. 73, no. 2 (1961), 295-323.
    • (1961) Ann. of Math. , vol.73 , Issue.2 , pp. 295-323
    • Palais, R.1
  • 30
    • 0003288058 scopus 로고
    • Critical point theory and submanifold geometry
    • Springer-Verlag, Berlin
    • R. S. PALAIS and C. L. TERNG, Critical point theory and submanifold geometry, Lecture Notes in Mathematics 1353, Springer-Verlag, Berlin, 1988.
    • (1988) Lecture Notes in Mathematics , vol.1353
    • Palais, R.S.1    Terng, C.L.2
  • 32
    • 0001379836 scopus 로고
    • Inequalities defining orbit spaces
    • G. PROCESI and G. SCHWARZ, Inequalities defining orbit spaces, Invent. Math. 81 (1985), 539-554.
    • (1985) Invent. Math. , vol.81 , pp. 539-554
    • Procesi, G.1    Schwarz, G.2
  • 34
    • 84972513491 scopus 로고
    • Gauss-Bonnet theorem for V-manifolds
    • I. SATAKE, Gauss-Bonnet theorem for V-manifolds, J. Math. Soc. Japan 9 (1957), 464-492.
    • (1957) J. Math. Soc. Japan , vol.9 , pp. 464-492
    • Satake, I.1
  • 35
    • 0042805662 scopus 로고
    • Smooth functions invariant under the action of a compact Lie group
    • G. W. SCHWARZ, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63-68.
    • (1975) Topology , vol.14 , pp. 63-68
    • Schwarz, G.W.1
  • 36
    • 51649161231 scopus 로고
    • Lifting smooth homotopies of orbit spaces
    • G. W. SCHWARZ, Lifting smooth homotopies of orbit spaces, Publ. Math. IHES 51 (1980), 37-136.
    • (1980) Publ. Math. IHES , vol.51 , pp. 37-136
    • Schwarz, G.W.1
  • 37
    • 0001229672 scopus 로고
    • Stratified symplectic spaces and reduction
    • R. SJAMAAR and E. LERMAN, Stratified symplectic spaces and reduction, Ann. Math. 134 (1991), 375-422.
    • (1991) Ann. Math. , vol.134 , pp. 375-422
    • Sjamaar, R.1    Lerman, E.2
  • 38
    • 0001705405 scopus 로고
    • Elementary structure of real algebraic varieties
    • H. WHITNEY, Elementary structure of real algebraic varieties, Ann. Math. 66 (1957), 545-556.
    • (1957) Ann. Math. , vol.66 , pp. 545-556
    • Whitney, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.