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Volumn 66, Issue 2, 2002, Pages 468-486

Jacobi fields along harmonic 2-spheres in ℂP2 are integrable

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EID: 0036807076     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610702003496     Document Type: Article
Times cited : (16)

References (39)
  • 1
    • 0000168026 scopus 로고
    • Rates of asymptotic convergence near isolated singularities of geometric extrema
    • D. Adams and L. Simon, 'Rates of asymptotic convergence near isolated singularities of geometric extrema', Indiana J. Math. 37 (1988) 225-254.
    • (1988) Indiana J. Math. , vol.37 , pp. 225-254
    • Adams, D.1    Simon, L.2
  • 5
    • 0011268391 scopus 로고
    • n, Harmonic maps
    • Proceedings, New Orleans, 1980, Springer, Berlin
    • n, Harmonic maps. Proceedings, New Orleans, 1980, Lecture Notes in Mathematics 949 (Springer, Berlin, 1982) 48-56.
    • (1982) Lecture Notes in Mathematics , vol.949 , pp. 48-56
    • Burns, D.1
  • 6
    • 84972514026 scopus 로고
    • The construction of harmonic maps into complex Grassmannians
    • F.E. Burstall and J.C. Wood, 'The construction of harmonic maps into complex Grassmannians', J. Differential Geom. 23 (1986) 255-297.
    • (1986) J. Differential Geom. , vol.23 , pp. 255-297
    • Burstall, F.E.1    Wood, J.C.2
  • 7
    • 84972528644 scopus 로고
    • Minimal immersions of surfaces in Euclidean spheres
    • E. Calabi, 'Minimal immersions of surfaces in Euclidean spheres', J. Differential Geom. 1 (1967) 111-125.
    • (1967) J. Differential Geom. , vol.1 , pp. 111-125
    • Calabi, E.1
  • 8
    • 0001838437 scopus 로고
    • Quelques applications de l'analyse-complexe aux surfaces d'aire minima
    • Université de Montréal
    • E. Calabi, 'Quelques applications de l'analyse-complexe aux surfaces d'aire minima', Topics in complex manifolds (Université de Montréal, 1967) 59-81.
    • (1967) Topics in complex manifolds , pp. 59-81
    • Calabi, E.1
  • 9
    • 0031231599 scopus 로고    scopus 로고
    • The space of harmonic maps from the 2-sphere to the complex projective plane
    • T.A. Crawford, 'The space of harmonic maps from the 2-sphere to the complex projective plane', Canad. Math. Bull. 40 (1997) 285-295.
    • (1997) Canad. Math. Bull. , vol.40 , pp. 285-295
    • Crawford, T.A.1
  • 13
    • 0000240898 scopus 로고
    • Another report on harmonic maps
    • J. Eells and L. Lemaire, 'Another report on harmonic maps', Bull. London Math. Soc. 20 (1988) 385-524.
    • (1988) Bull. London Math. Soc. , vol.20 , pp. 385-524
    • Eells, J.1    Lemaire, L.2
  • 14
    • 0000610931 scopus 로고
    • Harmonic maps from surfaces to complex projective spaces
    • J. Eells and J.C. Wood, 'Harmonic maps from surfaces to complex projective spaces', Adv. Math. 49 (1983) 217-263.
    • (1983) Adv. Math. , vol.49 , pp. 217-263
    • Eells, J.1    Wood, J.C.2
  • 15
    • 0001812542 scopus 로고
    • On the regularity of the minima of certain quadratic functionals
    • M. Giaquinta and E. Guisti, 'On the regularity of the minima of certain quadratic functionals', Acta Math. 148 (1982) 31-46.
    • (1982) Acta Math. , vol.148 , pp. 31-46
    • Giaquinta, M.1    Guisti, E.2
  • 16
    • 0002170931 scopus 로고
    • The singular set of the minima of certain quadratic functionals
    • M. Giaquinta and E. Guisti, 'The singular set of the minima of certain quadratic functionals', Ann. Scuola Norm. Sup. Pisa 11 (1984) 45-55.
    • (1984) Ann. Scuola Norm. Sup. Pisa , vol.11 , pp. 45-55
    • Giaquinta, M.1    Guisti, E.2
  • 18
    • 84972567966 scopus 로고
    • Group actions and deformations for harmonic maps
    • M.A. Guest and Y. Ohnita, 'Group actions and deformations for harmonic maps', J. Math. Soc. Japan 45 (1993) 671-704.
    • (1993) J. Math. Soc. Japan , vol.45 , pp. 671-704
    • Guest, M.A.1    Ohnita, Y.2
  • 19
    • 0000574713 scopus 로고
    • The rate of convergence of a harmonic map at a singular point
    • R. Gulliver and B. White, 'The rate of convergence of a harmonic map at a singular point', Math. Ann. 283 (1989) 539-549.
    • (1989) Math. Ann. , vol.283 , pp. 539-549
    • Gulliver, R.1    White, B.2
  • 20
    • 0000408314 scopus 로고
    • A theory of branched immersions of surfaces
    • R.D. Gulliver, R. Osserman and H.L. Royden, 'A theory of branched immersions of surfaces', Amer. J. Math. 95 (1973) 750-812.
    • (1973) Amer. J. Math. , vol.95 , pp. 750-812
    • Gulliver, R.D.1    Osserman, R.2    Royden, H.L.3
  • 21
    • 0031540281 scopus 로고    scopus 로고
    • Singularities of harmonic maps
    • R.M. Hardt, 'Singularities of harmonic maps', Bull. Amer. Math. Soc. 34 (1997) 15-34.
    • (1997) Bull. Amer. Math. Soc. , vol.34 , pp. 15-34
    • Hardt, R.M.1
  • 22
    • 0002442550 scopus 로고
    • An existence theorem for harmonic mappings of Riemannian manifolds
    • H. Hildebrandt, H. Kaul and K.-O. Widman, 'An existence theorem for harmonic mappings of Riemannian manifolds', Acta Math. 138 (1977) 1-16.
    • (1977) Acta Math. , vol.138 , pp. 1-16
    • Hildebrandt, H.1    Kaul, H.2    Widman, K.-O.3
  • 23
    • 0002943709 scopus 로고
    • Uniqueness and stability of harmonic maps, and their Jacobi fields
    • W. Jäger and H. Kaul, 'Uniqueness and stability of harmonic maps, and their Jacobi fields', Manuscripts Math. 28 (1979) 262-291.
    • (1979) Manuscripts Math. , vol.28 , pp. 262-291
    • Jäger, W.1    Kaul, H.2
  • 25
    • 84948728111 scopus 로고
    • Sar certaines structures fibrées complexes
    • J.L. Koszul and B. Malgrange, 'Sar certaines structures fibrées complexes', Arch. Math. 9 (1958) 102-109.
    • (1958) Arch. Math. , vol.9 , pp. 102-109
    • Koszul, J.L.1    Malgrange, B.2
  • 27
    • 84968486083 scopus 로고
    • On the integrability of Jacobi fields on minimal surfaces
    • D.S.P. Leung, 'On the integrability of Jacobi fields on minimal surfaces', Trans. Amer. Math. Soc. 220 (1976) 185-194.
    • (1976) Trans. Amer. Math. Soc. , vol.220 , pp. 185-194
    • Leung, D.S.P.1
  • 28
    • 21744436414 scopus 로고    scopus 로고
    • Second variation of superminimal surfaces into self-dual Einstein four-manifolds
    • S. Montiel and F. Urbano, 'Second variation of superminimal surfaces into self-dual Einstein four-manifolds', Trans. Amer. Math. Soc. 349 (1997) 2253-2269.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 2253-2269
    • Montiel, S.1    Urbano, F.2
  • 29
    • 0011273399 scopus 로고    scopus 로고
    • The deformation of harmonic maps given by the Clifford tori
    • M. Mukai, 'The deformation of harmonic maps given by the Clifford tori', Kodai Math. J. 20 (1997) 252-268.
    • (1997) Kodai Math. J. , vol.20 , pp. 252-268
    • Mukai, M.1
  • 30
    • 84972544463 scopus 로고
    • A regularity theory for harmonic maps
    • R. Schoen and K. Uhlenbeck, 'A regularity theory for harmonic maps', J. Differential Geom. 17 (1982) 307-335; 18 (1983) 329.
    • (1982) J. Differential Geom. , vol.17 , pp. 307-335
    • Schoen, R.1    Uhlenbeck, K.2
  • 32
    • 0000137102 scopus 로고
    • Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
    • L. Simon, 'Asymptotics for a class of non-linear evolution equations, with applications to geometric problems', Ann. of Math. 118 (1983) 525-571.
    • (1983) Ann. of Math. , vol.118 , pp. 525-571
    • Simon, L.1
  • 33
    • 0011311867 scopus 로고
    • Isolated singularities of extrema of geometric variational problems
    • Harmonic mappings and minimal immersions (Montecatini), Springer, Berlin
    • L. Simon, 'Isolated singularities of extrema of geometric variational problems', Harmonic mappings and minimal immersions (Montecatini, 1984), Lecture Notes in Mathematics 1161 (Springer, Berlin, 1985) 206-277.
    • (1984) Lecture Notes in Mathematics , vol.1161 , pp. 206-277
    • Simon, L.1
  • 34
    • 84972531248 scopus 로고
    • Cylindrical tangent cones and the singular set of minimal submanifolds
    • L. Simon, 'Cylindrical tangent cones and the singular set of minimal submanifolds', J. Differential Geom. 38 (1993) 585-652.
    • (1993) J. Differential Geom. , vol.38 , pp. 585-652
    • Simon, L.1
  • 35
    • 0003374625 scopus 로고
    • Rectifiability of the singular set of energy minimizing maps
    • L. Simon, 'Rectifiability of the singular set of energy minimizing maps', Calc. Var. Partial Differential Equations 3 (1995) 1-65.
    • (1995) Calc. Var. Partial Differential Equations , vol.3 , pp. 1-65
    • Simon, L.1
  • 36
    • 0003988481 scopus 로고    scopus 로고
    • Theorems on regularity and singularity of energy minimizing maps
    • Birkhäuser
    • L. Simon, Theorems on regularity and singularity of energy minimizing maps, ETH Zürich Lecture Notes in Mathematics (Birkhäuser, 1996).
    • (1996) ETH Zürich Lecture Notes in Mathematics
    • Simon, L.1
  • 37
    • 0011363485 scopus 로고
    • Rigidity of certain harmonic mappings
    • T. Sunada, 'Rigidity of certain harmonic mappings', Invent. Math. 51 (1979) 297-307.
    • (1979) Invent. Math. , vol.51 , pp. 297-307
    • Sunada, T.1
  • 38
    • 85027235032 scopus 로고    scopus 로고
    • Jacobi fields along harmonic maps
    • Differential geometry and integrable systems. Tokyo, Contemp. Math., to appear
    • J.C. Wood, 'Jacobi fields along harmonic maps', Differential geometry and integrable systems. Proceedings of the 9th MSJ-IRI, Tokyo, 2000 (Contemp. Math., to appear).
    • (2000) Proceedings of the 9th MSJ-IRI
    • Wood, J.C.1
  • 39
    • 0011316962 scopus 로고
    • The free loop space of globally symmetric spaces
    • W. Ziller, 'The free loop space of globally symmetric spaces', Invent. Math. 41 (1977) 1-22.
    • (1977) Invent. Math. , vol.41 , pp. 1-22
    • Ziller, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.