메뉴 건너뛰기




Volumn 48, Issue 4, 2004, Pages 1191-1206

The exponential map of a weak Riemannian Hilbert manifold

Author keywords

[No Author keywords available]

Indexed keywords


EID: 17244375136     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1258138506     Document Type: Article
Times cited : (9)

References (23)
  • 1
    • 0003321363 scopus 로고
    • Manifolds, tensor analysis, and applications
    • Springer-Verlag, New York. MR 960687 (89f:58001)
    • R. Abraham, J. E. Marsden, and T. Ratiu, Manifolds, tensor analysis, and applications, Applied Mathematical Sciences, vol. 75, Springer-Verlag, New York, 1988. MR 960687 (89f:58001)
    • (1988) Applied Mathematical Sciences , vol.75
    • Abraham, R.1    Marsden, J.E.2    Ratiu, T.3
  • 2
    • 17244375207 scopus 로고
    • The Cartan structural equations in classical Riemannian geometry
    • MR 0123996 (23 #A1317)
    • W. Ambrose, The Cartan structural equations in classical Riemannian geometry, J. Indian Math. Soc. (N.S.) 24 (1960), 23-76 (1961). MR 0123996 (23 #A1317)
    • (1960) J. Indian Math. Soc. (N.S.) , vol.24 , pp. 23-76
    • Ambrose, W.1
  • 3
    • 0001356905 scopus 로고
    • Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits
    • MR 0202082 (34 #1956)
    • V. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble) 16 (1966), 319-361. MR 0202082 (34 #1956)
    • (1966) Ann. Inst. Fourier (Grenoble) , vol.16 , pp. 319-361
    • Arnold, V.1
  • 5
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the notion of an incompressible fluid
    • MR 0271984 (42 #6865)
    • D. G. Ebin and J. Marsden, Groups of diffeomorphisms and the notion of an incompressible fluid., Ann. of Math. (2) 92 (1970), 102-163. MR 0271984 (42 #6865)
    • (1970) Ann. of Math. (2) , vol.92 , pp. 102-163
    • Ebin, D.G.1    Marsden, J.2
  • 6
    • 0002766050 scopus 로고
    • Differential structures and Fredholm maps on Banach manifolds
    • (Berkeley, Calif.), Amer, Math. Soc., Providence, R.I. MR 0264708 (41 #9299)
    • K. D. Elworthy and A. J. Tromba, Differential structures and Fredholm maps on Banach manifolds, Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968), Amer, Math. Soc., Providence, R.I., 1970, pp. 45-94. MR 0264708 (41 #9299)
    • (1968) Global Analysis (Proc. Sympos. Pure Math.) , vol.15 , pp. 45-94
    • Elworthy, K.D.1    Tromba, A.J.2
  • 7
    • 84972518061 scopus 로고
    • The geometry of loop groups
    • MR 961515 (89k:22036)
    • D. S. Freed, The geometry of loop groups, J. Differential Geom. 28 (1988), 223- 276. MR 961515 (89k:22036)
    • (1988) J. Differential Geom. , vol.28 , pp. 223-276
    • Freed, D.S.1
  • 8
    • 84968505013 scopus 로고
    • Hilbert manifolds without epiconjugate points
    • MR 0188943 (32 #6370)
    • N. Grossman, Hilbert manifolds without epiconjugate points, Proc. Amer. Math. Soc. 16 (1965), 1365-1371. MR 0188943 (32 #6370)
    • (1965) Proc. Amer. Math. Soc. , vol.16 , pp. 1365-1371
    • Grossman, N.1
  • 9
    • 0003245418 scopus 로고
    • Differential geometry. Lie groups, and symmetric spaces
    • Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York. MR 514561 (80k:53081)
    • S. Helgason, Differential geometry. Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1978. MR 514561 (80k:53081)
    • (1978) Pure and Applied Mathematics , vol.80
    • Helgason, S.1
  • 10
    • 84980162923 scopus 로고
    • Riemannian center of mass and mollifier smoothing
    • MR 0442975 (56 #1350)
    • H. Karcher, Riemannian center of mass and mollifier smoothing, Comm. Pure Appl. Math. 30 (1977), 509-541. MR 0442975 (56 #1350)
    • (1977) Comm. Pure Appl. Math. , vol.30 , pp. 509-541
    • Karcher, H.1
  • 11
    • 17244369567 scopus 로고
    • Riemannian geometry
    • Walter de Gruyter & Co., Berlin. MR 1330918 (95m:53003)
    • W. P. A. Klingenberg, Riemannian geometry, de Gruyter Studies in Mathematics, vol. 1, Walter de Gruyter & Co., Berlin, 1995. MR 1330918 (95m:53003)
    • (1995) De Gruyter Studies in Mathematics , vol.1
    • Klingenberg, W.P.A.1
  • 12
    • 0004341311 scopus 로고
    • Interscience Publishers, a division of John Wiley & Sons, New York-Lond on. MR 0152974 (27 #2945)
    • S. Kobayashi and K. Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York-Lond on, 1963. MR 0152974 (27 #2945)
    • (1963) Foundations of Differential Geometry , vol.1
    • Kobayashi, S.1    Nomizu, K.2
  • 13
    • 0003267328 scopus 로고
    • Differential and Riemannian manifolds
    • Springer-Verlag, New York. MR 1335233 (96d:53001)
    • S. Lang, Differential and Riemannian manifolds, Graduate Texts in Mathematics, vol. 160, Springer-Verlag, New York, 1995. MR 1335233 (96d:53001)
    • (1995) Graduate Texts in Mathematics , vol.160
    • Lang, S.1
  • 14
    • 0003252211 scopus 로고
    • Morse theory
    • Based on lecture notes by M. Spivak and R. Wells. Princeton University Press, Princeton, N.J. MR 0163331 (29 #634)
    • J. Milnor, Morse theory, Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. MR 0163331 (29 #634)
    • (1963) Annals of Mathematics Studies , vol.51
    • Milnor, J.1
  • 15
    • 0001582143 scopus 로고
    • Curvatures of left invariant metrics on Lie groups
    • MR0425012(54#12970)
    • J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), 293-329. MR 0425012 (54 #12970)
    • (1976) Advances in Math. , vol.21 , pp. 293-329
    • Milnor, J.1
  • 16
    • 0031285558 scopus 로고    scopus 로고
    • The exponential map on the free loop space is Fredholm
    • MR 1475552 (98e:58018)
    • G. Misiolek, The exponential map on the free loop space is Fredholm, Geom. Funct. Anal. 7 (1997), 1-17. MR 1475552 (98e:58018)
    • (1997) Geom. Funct. Anal. , vol.7 , pp. 1-17
    • Misiolek, G.1
  • 17
    • 22644452021 scopus 로고    scopus 로고
    • Exponential maps of Sobolev metrics on loop groups
    • MR 1626450 (99j:58015)
    • _, Exponential maps of Sobolev metrics on loop groups, Proc. Amer. Math. Soc 127 (1999), 2475-2482. MR 1626450 (99j:58015)
    • (1999) Proc. Amer. Math. Soc , vol.127 , pp. 2475-2482
  • 18
    • 21344433327 scopus 로고    scopus 로고
    • 2)
    • MR 1301038 (96f:58009)
    • 2), Proc. Amer. Math. Soc. 124 (1996), 977-982. MR 1301038 (96f:58009)
    • (1996) Proc. Amer. Math. Soc. , vol.124 , pp. 977-982
  • 19
    • 0001674071 scopus 로고
    • Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms
    • MR 1218713 (94j:58027)
    • _, Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms, Indiana Univ. Math. J. 42 (1993), 215-235. MR 1218713 (94j:58027)
    • (1993) Indiana Univ. Math. J. , vol.42 , pp. 215-235
  • 20
    • 0003329298 scopus 로고
    • Loop groups
    • The Clarendon Press Oxford University Press, New York. MR 900587 (88i:22049)
    • A. Pressley and G. Segal, Loop groups, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1986. MR 900587 (88i:22049)
    • (1986) Oxford Mathematical Monographs
    • Pressley, A.1    Segal, G.2
  • 22
    • 0003230647 scopus 로고    scopus 로고
    • Riemannian geometry
    • American Mathematical Society, Providence, RI. MR 1390760 (97f:53001)
    • T. Sakai, Riemannian geometry, Translations of Mathematical Monographs, vol. 149, American Mathematical Society, Providence, RI, 1996. MR 1390760 (97f:53001)
    • (1996) Translations of Mathematical Monographs , vol.149
    • Sakai, T.1
  • 23
    • 0001146482 scopus 로고
    • An infinite dimensional version of Sard's theorem
    • MR 0185604 (32 #3067)
    • S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1965), 861-866. MR 0185604 (32 #3067)
    • (1965) Amer. J. Math. , vol.87 , pp. 861-866
    • Smale, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.