Willmore two-spheres in the four-sphere

Transactions of the American Mathematical Society

Volumn 352, Issue 10, 2000, Pages 4469-4486

  Montiel, Sebastian ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Minimal surface; Willmore surface

Indexed keywords

EID: 23044522050     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02571-x     Document Type: Article

References (27)

1. [B1] W. Blaschkc, Vorlesungen Über Differentialgeometrie III, Springer, Berlin, 1929.
2. [Br1] R.L. Bryant, A duality theorem for Willmore surfaces, J. of Diff. Geom., 20(1984), 23-53. MR 86j:58029
3. [Br2] R.L. Bryant, Surfaces in conformai geometry, Proc. of Symp. in Pure Math., 48(1988), 227-240. MR 89m:53102
4. [CU] I. Castro, F. Urbano, Lagrangian surfaces in the complex Euclidean plane with conformai Maslov form, Tôhoku Math. J., 45(1993), 565-582. MR 94j:530G4
5. [E] N. Bjiri, Willmore surfaces with a duality in SN(1), Proc. London Math. Soc., 57(1988), 383-416. MR 89h:53117
6. [ES] J. Eclls, S. Salamon, Twistorial constructions of harmonie maps of surfaces into fourmanifolds, Ann. Scuola Norm. Sup. Pisa, 12(1985), 589-640. MR 87i:58042
7. [F] T. Friedrich, On surfaces in four-spaces, Ann. Global Anal. Geom., 2(1984), 257-287. MR 86h:53061
8. [GH] P. Griffiths, J. Harris, Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978. MR 80b:14001
9. [Hi] M.W. Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc., 93(1959), 242-276. MR 22:9980
10. [HO] D. Huffman, R. Osserman, The geometry of the generalized Gauss map, Mem. Amer. Math. Soc., 236(1980). MR 82b:53012
11. [KM] J.L. Koszul, B. Malgrangc, Sur certaines structures fibres complexes, Arch. Math., 9(1958), 102-109. MR 24:A1729
12. [K1] R. Kusner, Conformai geometry and complete minimal surfaces, Bull. Amer. Math. Soc., 17(1987), 291-295. MR 88j:53008
13. [K2] R. Kusner, Comparison surfaces for the Willmore problem, Pacific Math. J., 138(1989), 317-345. MR 90e:53013
14. [KS] R. Kusner, N. Schmitt, The spinor representation of surfaces in space, preprint.
15. [LS] R. Lashof, S. Smale, On immersions of manifolds in Euclidean space, Ann. of Math., 68(1958), 562-583. MR 21:2246
16. [LY] P. Li, S.T. Yau, A new conformai invariant and its applications to the Willmore conjecture and first eigenvalue, of compact surf aces, Invent. Math., 69(1982), 269-291. MR84f:53049
17. [ MR] S. Montiel, A. Romcro, Complex Einstein hypersurfaces of indefinite complex space forms, Math. Proc. Cambridge Phil. Soc., 93(1983), 495-508. MR 85f:53049
18. [ MRo] S. Montiel, A. Ros, Minimal immersions of surfaces by the first eigenfunctions and conformal area, Invent. Math., 83(1986), 153-166. MR 87d:53109
19. [R] A. Ros, The Willmore conjecture in the real projective space, Math. Res. Lett. 6 (1999), 487-493. - .
20. [RT] H. Rosenberg, E. Toubiana, Some remarks on deformations of minimal surfaces, Trans. Amer. Math. Soc., 295(1986), 491-499. MR 88a:53005b
21. [S] S. Salamon, Topics in four-dimensional Riemannian geometry, Lecture Notes in Mathematics, 1022(1982), 34-124. MR 851:53002
22. [We] J.L. Weiner, On an inequality of P. Wintgen for the integral of the square of the mean curvature, J. London Math. Soc., 34(1986), 148-158. MR 87k:53147
23. [Wei] A. Weinstein, Lectures on symplectic manifolds, Conf. Board Math. Sei., Regional Conf. Ser. Math., vol. 29, Amer. Math. Soc., Providence, RI, 1977. MR 57:4244
24. [Wil] T.J. Willmore, Note on embedded surfaces, An. Sti. Univ. "Al. I. Cuza" lasi Sect. I a Mat., 11(1965), 493-496. MR 34:1940
25. [Wi2] T.J. Willmore, Mean curvature of Riemannian immersions, J. London Math. Soc., 3(1971), 307-310. MR 44:959
26. [Win] P. Wintgen, On the total curvature of surfaces in E4, Colloq. Math., 39(1978), 289-296. MR 80f:53037
27. [Wo] J.A. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York, 1967. MR 36:829