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Volumn 349, Issue 6, 1997, Pages 2253-2269

Second variation of superminimal surfaces into self-dual einstein four-manifolds

Author keywords

Index; Nullity; Superminimal surfaces

Indexed keywords


EID: 21744436414     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01933-8     Document Type: Article
Times cited : (25)

References (32)
  • 1
    • 0000018889 scopus 로고
    • Self-duality in four-dimensional Riemannian geometry
    • [AHS] MR 80d:53023
    • [AHS] M.F. Atiyah, N.J. Hitchin, I.M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A, 362(1978), 425-461. MR 80d:53023
    • (1978) Proc. Roy. Soc. London Ser. a , vol.362 , pp. 425-461
    • Atiyah, M.F.1    Hitchin, N.J.2    Singer, I.M.3
  • 2
    • 84956262923 scopus 로고
    • On minimal immersions of S2 into S2m
    • [B] MR 51:11362
    • [B] J.L.M. Barbosa, On minimal immersions of S2 into S2m, Trans. Amer. Math. Soc., 210(1975), 75-106. MR 51:11362
    • (1975) Trans. Amer. Math. Soc. , vol.210 , pp. 75-106
    • Barbosa, J.L.M.1
  • 4
    • 0004058055 scopus 로고
    • [Be2] Springer-Verlag, Berlin. MR 88f:53087
    • [Be2] A.L. Besse, Einstein Manifolds, Springer-Verlag, 1987, Berlin. MR 88f:53087
    • (1987) Einstein Manifolds
    • Besse, A.L.1
  • 5
    • 84972503061 scopus 로고
    • Conformai and minimal immersions of compact surfaces into the 4-sphere
    • [Br] MR 84a:53062
    • [Br] R.L. Bryant, Conformai and minimal immersions of compact surfaces into the 4-sphere, J. Differential Geometry, 17(1982), 455-473. MR 84a:53062
    • (1982) J. Differential Geometry , vol.17 , pp. 455-473
    • Bryant, R.L.1
  • 6
    • 84972519697 scopus 로고
    • Some decompositions of the space of symmetric tensors on a Riemannian manifold
    • [BE] MR 42:993
    • [BE] M. Berger, D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold, J. Differential Geometry, 3(1969), 379-392. MR 42:993
    • (1969) J. Differential Geometry , vol.3 , pp. 379-392
    • Berger, M.1    Ebin, D.2
  • 7
    • 84972528644 scopus 로고
    • Minimal immersions of surfaces in Euclidean spheres, 3
    • [C] MR 38:1616
    • [C] E. Calabi, Minimal immersions of surfaces in Euclidean spheres, 3. Differential Geometry, 1(1967), 111-125. MR 38:1616
    • (1967) Differential Geometry , vol.1 , pp. 111-125
    • Calabi, E.1
  • 9
    • 0002585508 scopus 로고
    • Minimal surfaces by moving frames
    • [CheW] MR 84i:53056
    • [CheW] S.S. Chern, J.G. Wolfson, Minimal surfaces by moving frames, Amer. J. Math., 105(1983), 59-83. MR 84i:53056
    • (1983) Amer. J. Math. , vol.105 , pp. 59-83
    • Chern, S.S.1    Wolfson, J.G.2
  • 10
    • 0242673510 scopus 로고
    • The index of minimal immersions o/S2 into S2tl
    • [E] MR 85b:53062
    • [E] N. Ejiri, The index of minimal immersions o/S2 into S2tl, Math. Z., 184(1983), 127-132. MR 85b:53062
    • (1983) Math. Z. , vol.184 , pp. 127-132
    • Ejiri, N.1
  • 11
    • 0000818374 scopus 로고
    • Twistorial constructions of harmonic maps of surfaces into fourmanifolds
    • [ES] MR 87i:58042
    • [ES] J. Eells, S. Salamon, Twistorial constructions of harmonic maps of surfaces into fourmanifolds, Ann. Scuola Norm. Sup. Pisa, 12(1985), 589-640. MR 87i:58042
    • (1985) Ann. Scuola Norm. Sup. Pisa , vol.12 , pp. 589-640
    • Eells, J.1    Salamon, S.2
  • 12
    • 0000164159 scopus 로고
    • The fundamental equations of minimal surfaces in C?2
    • [EGT] MR 8Gm:58041
    • [EGT] J.H. Eschenburg, I.V. Guadalupe, R.A. Tribuzy, The fundamental equations of minimal surfaces in C?2 , Math. Ann., 270(1985), 571-598. MR 8Gm:58041
    • (1985) Math. Ann. , vol.270 , pp. 571-598
    • Eschenburg, J.H.1    Guadalupe, I.V.2    Tribuzy, R.A.3
  • 13
    • 0000362154 scopus 로고
    • On complete minimal surfaces with finite Morse index in threemanifolds
    • [FC] MR 87b:53090
    • [FC] D. Fischer-Colbrie, On complete minimal surfaces with finite Morse index in threemanifolds. Invent. Math., 82(1985), 121-132. MR 87b:53090
    • (1985) Invent. Math. , vol.82 , pp. 121-132
    • Fischer-Colbrie, D.1
  • 14
    • 84980187204 scopus 로고
    • The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
    • [FCS] MR 81i:53044
    • [FCS] D. Fischer-Colbrie,. R. Schoen, The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature, Comm. Pure Appl. Math., 33(1980), 199- 211. MR 81i:53044
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 199-211
    • Fischer-Colbrie, D.1    Schoen, R.2
  • 15
    • 0039863425 scopus 로고
    • On surfaces in four-spaces
    • [Fr] MR 86h:530G
    • [Fr] T. Friedrich, On surfaces in four-spaces, Ann. Global Anal. Geom., 2(1984), 257-287. MR 86h:530G
    • (1984) Ann. Global Anal. Geom. , vol.2 , pp. 257-287
    • Friedrich, T.1
  • 16
    • 84985305138 scopus 로고
    • On Einstein metrics on the twistor space of a fourdimensional Riemannian manifold
    • [FrG] MR 87c:53093
    • [FrG] T. Friedrich, R. Grünewald, On Einstein metrics on the twistor space of a fourdimensional Riemannian manifold, Math. Nachr., 123(1985), 55-60. MR 87c:53093
    • (1985) Math. Nachr. , vol.123 , pp. 55-60
    • Friedrich, T.1    Grünewald, R.2
  • 17
    • 4243468415 scopus 로고
    • Les immersions super-minimales d'une surface compacte dans une variété riemannienne orientée de dimension 4
    • [G] MR 89g:58052
    • [G] P. Gauduchon, Les immersions super-minimales d'une surface compacte dans une variété riemannienne orientée de dimension 4, Astérisque, 154-155(1987), 151-180. MR 89g:58052
    • (1987) Astérisque , vol.154-155 , pp. 151-180
    • Gauduchon, P.1
  • 19
    • 84959731878 scopus 로고
    • Kählerian twistor spaces
    • [H] MR 84b:32014
    • [H] N.J. Hitchin, Kählerian twistor spaces, Proc. Lond. Math. Soc., 43(1981), 133-150. MR 84b:32014
    • (1981) Proc. Lond. Math. Soc. , vol.43 , pp. 133-150
    • Hitchin, N.J.1
  • 20
    • 84966208412 scopus 로고
    • Connectedness of the space of minimal 2-spheres in S"(l)
    • [K] MR 94e:58033
    • [K] M. Kotani, Connectedness of the space of minimal 2-spheres in S"(l)., Proc. Amer. Math. Soc., 120(1994), 803-810. MR 94e:58033
    • (1994) Proc. Amer. Math. Soc. , vol.120 , pp. 803-810
    • Kotani, M.1
  • 21
    • 84948728111 scopus 로고
    • Sur certaines structures fibrées complexes
    • [KM] MR 24:A1729
    • [KM] J.L. Koszul, B. Malgrange, Sur certaines structures fibrées complexes, Arch. Math., 9(1958), 102-109. MR 24:A1729
    • (1958) Arch. Math. , vol.9 , pp. 102-109
    • Koszul, J.L.1    Malgrange, B.2
  • 22
  • 23
    • 84966248758 scopus 로고
    • The space of harmonic maps o/S2 into S4
    • [Lo] MR 90k:58050
    • [Lo] B. Loo, The space of harmonic maps o/S2 into S4, Trans. Amer. Math. Soc., 313(1989), 81-102. MR 90k:58050
    • (1989) Trans. Amer. Math. Soc. , vol.313 , pp. 81-102
    • Loo, B.1
  • 24
    • 0001275934 scopus 로고
    • Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic twp-planes
    • [MM] MR 89e:53088
    • [MM] M. J. Micallef, J.D. Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic twp-planes, Ann. of Math., 127(1988), 199-227. MR 89e:53088
    • (1988) Ann. of Math. , vol.127 , pp. 199-227
    • Micallef, M.J.1    Moore, J.D.2
  • 25
    • 0000592987 scopus 로고
    • The second variation of area of minimal surfaces in fourmanifolds
    • [M\V] MR 94c:58035
    • [M\V] M. J. Micallef, J.G. Wolfson, The second variation of area of minimal surfaces in fourmanifolds, Math. Ann., 295(1993), 245-267. MR 94c:58035
    • (1993) Math. Ann. , vol.295 , pp. 245-267
    • Micallef, M.J.1    Wolfson, J.G.2
  • 26
    • 0000466791 scopus 로고
    • Schrödinger operators associated to a holomorphic map
    • [MoR] MR 93k:58053
    • [MoR] S. Montiel, A. Ros, Schrödinger operators associated to a holomorphic map, Lecture Notes in Mathematics, 1481(1991), 147-174. MR 93k:58053
    • (1991) Lecture Notes in Mathematics , vol.1481 , pp. 147-174
    • Montiel, S.1    Ros, A.2
  • 27
    • 0000571272 scopus 로고
    • Second variation and stabilities of minimal Lagrangian submanifolds in Kahler manifolds
    • [O] MR 91f:58022
    • [O] Y.G. Oh, Second variation and stabilities of minimal Lagrangian submanifolds in Kahler manifolds, Invent. Math., 101(1990), 501-519. MR 91f:58022
    • (1990) Invent. Math. , vol.101 , pp. 501-519
    • Oh, Y.G.1
  • 28
    • 0001593830 scopus 로고
    • Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
    • [SY] MR 81k:58029
    • [SY] R. Schoen, S.T. Yau, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature, Ann. of Math., 110(1979), 127-142. MR 81k:58029
    • (1979) Ann. of Math. , vol.110 , pp. 127-142
    • Schoen, R.1    Yau, S.T.2
  • 29
    • 0008711177 scopus 로고
    • Topics in four-dimensional Riemannian geometry
    • [Sa] MR 85J-.53002
    • [Sa] S. Salamon, Topics in four-dimensional Riemannian geometry, Lectures Notes in Mathematics, 1022(1982), 34-124. MR 85J-.53002
    • (1982) Lectures Notes in Mathematics , vol.1022 , pp. 34-124
    • Salamon, S.1
  • 30
    • 0002460686 scopus 로고
    • Minimal varieties in Riemaniann manifolds
    • [Si]
    • [Si] J. Simons, Minimal varieties in Riemaniann manifolds, Ann. of Math., 88(1968), 62-105
    • (1968) Ann. of Math. , vol.88 , pp. 62-105
    • Simons, J.1
  • 31
    • 0001080290 scopus 로고
    • Compact Kahler manifolds of positive bisectional curvature
    • [SiuY] MR 81h:58029
    • [SiuY] Y.T. Siu, S.T. Yau, Compact Kahler manifolds of positive bisectional curvature, Invent. Math., 59(1980), 189-204. MR 81h:58029
    • (1980) Invent. Math. , vol.59 , pp. 189-204
    • Siu, Y.T.1    Yau, S.T.2
  • 32
    • 84966230066 scopus 로고
    • Minimal surfaces with low index in the three-dimensional sphere
    • [U] MR 90h:53073
    • [U] F. Urbano, Minimal surfaces with low index in the three-dimensional sphere, Proc. Amer. Math. Soc., 108(1990), 989-992. MR 90h:53073
    • (1990) Proc. Amer. Math. Soc. , vol.108 , pp. 989-992
    • Urbano, F.1


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