Horizontal holomorphic curves in $\textrm {Sp}(n)$-flag manifolds
HTML articles powered by AMS MathViewer
- by Kichoon Yang PDF
- Proc. Amer. Math. Soc. 103 (1988), 265-273 Request permission
Abstract:
A complete description of horizontal holomorphic curves in ${\text {Sp}}\left ( n \right )$-flag manifolds is given. For compact curves a Plücker type integral formula is derived.References
- Theodor Bröcker and Tammo tom Dieck, Representations of compact Lie groups, Graduate Texts in Mathematics, vol. 98, Springer-Verlag, New York, 1985. MR 781344, DOI 10.1007/978-3-662-12918-0
- A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458–538. MR 102800, DOI 10.2307/2372795
- Robert L. Bryant, Lie groups and twistor spaces, Duke Math. J. 52 (1985), no. 1, 223–261. MR 791300, DOI 10.1215/S0012-7094-85-05213-5
- F. E. Burstall, A twistor description of harmonic maps of a $2$-sphere into a Grassmannian, Math. Ann. 274 (1986), no. 1, 61–74. MR 834106, DOI 10.1007/BF01458017
- Shiing Shen Chern, On the minimal immersions of the two-sphere in a space of constant curvature, Problems in analysis (Lectures at the Sympos. in honor of Salomon Bochner, Princeton Univ., Princeton, N.J., 1969) Princeton Univ. Press, Princeton, N.J., 1970, pp. 27–40. MR 0362151
- Shiing Shen Chern, Selected papers, Springer-Verlag, New York-Heidelberg, 1978. With a foreword by H. Wu [Hung Hsi Wu] and introductory articles by André Weil and Phillip A. Griffiths. MR 514211
- Shiing Shen Chern, Complex manifolds without potential theory, 2nd ed., Universitext, Springer-Verlag, New York-Heidelberg, 1979. With an appendix on the geometry of characteristic classes. MR 533884, DOI 10.1007/978-1-4684-9344-3
- Shiing Shen Chern and Jon Gordon Wolfson, Minimal surfaces by moving frames, Amer. J. Math. 105 (1983), no. 1, 59–83. MR 692106, DOI 10.2307/2374381
- J. Eells and J. C. Wood, Harmonic maps from surfaces to complex projective spaces, Adv. in Math. 49 (1983), no. 3, 217–263. MR 716372, DOI 10.1016/0001-8708(83)90062-2
- James F. Glazebrook, The construction of a class of harmonic maps to quaternionic projective space, J. London Math. Soc. (2) 30 (1984), no. 1, 151–159. MR 760884, DOI 10.1112/jlms/s2-30.1.151
- Gary R. Jensen, Marco Rigoli, and Kichoon Yang, Holomorphic curves in the complex quadric, Bull. Austral. Math. Soc. 35 (1987), no. 1, 125–148. MR 875513, DOI 10.1017/S0004972700013095
- Simon Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982), no. 1, 143–171. MR 664330, DOI 10.1007/BF01393378
- Hsien-Chung Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math. 76 (1954), 1–32. MR 66011, DOI 10.2307/2372397
- Kichoon Yang, Frenet formulae for holomorphic curves in the two-quadric, Bull. Austral. Math. Soc. 33 (1986), no. 2, 195–206. MR 832521, DOI 10.1017/S0004972700003063
- Kichoon Yang, Almost complex homogeneous spaces and their submanifolds, World Scientific Publishing Co., Singapore, 1987. MR 938098, DOI 10.1142/0455
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 265-273
- MSC: Primary 53C42; Secondary 58E20
- DOI: https://doi.org/10.1090/S0002-9939-1988-0938681-0
- MathSciNet review: 938681