Skip to main content
×
×
Home

A Space of Harmonic Maps from a Sphere into the Complex Projective Space

  • Hiroko Kawabe (a1)
Abstract

Guest–Ohnita and Crawford have shown the path-connectedness of the space of harmonic maps from S2 to CPn of a fixed degree and energy. It is well known that the ∂ transform is defined on this space. In this paper, we will show that the space is decomposed into mutually disjoint connected subspaces on which ∂ is homeomorphic.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A Space of Harmonic Maps from a Sphere into the Complex Projective Space
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      A Space of Harmonic Maps from a Sphere into the Complex Projective Space
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      A Space of Harmonic Maps from a Sphere into the Complex Projective Space
      Available formats
      ×
Copyright
References
Hide All
[CW] Chern, S. S. and G.Wolfson, J., Harmonic maps of the two-sphere into a complex Grassmann manifold II*. Ann. of Math. 125(1987), no. 2, 301335. http://dx.doi.org/10.2307/1971312
[C] Crawford, T. A., The space of harmonic maps from the 2-sphere to the complex projective plane. Canad. Math. Bull. 40(1997), no. 3, 285295. http://dx.doi.org/10.4153/CMB-1997-035-4
[EW] Eells, J. and Wood, J. C., Harmonic maps from surfaces to complex projective spaces. Adv. in Math. 49(1983), no. 3, 217263. http://dx.doi.org/10.1016/0001-8708(83)90062-2
[GH] Griffiths, P. and Harris, J., Principles of algebraic geometry. Pure and Applied Mathematics, Wiley-Interscience, New York, 1978.
[GO] Guest, M. A. and Ohnita, Y., Group actions and deformations for harmonic maps. J. Math. Soc. Japan 45(1993), no. 4, 671704. http://dx.doi.org/10.2969/jmsj/04540671
[K] Kawabe, H., Harmonic maps from the Riemann sphere into the complex projective space and the harmonic sequences. Kodai Math. J. 33(2010), no. 3, 367382. http://dx.doi.org/10.2996/kmj/1288962548
[KN] Kobayashi, S. and Nomizu, K., Foundations of differential geometry. Vol. I and Vol. II, JohnWiley & Sons, Inc., New York, 1996.
[LW1] Lemaire, L. and C.Wood, J., On the space of harmonic 2-spheres in CP2. Internat. J. Math. 7(1996), no. 2, 211225. http://dx.doi.org/10.1142/S0129167X96000128
[LW2] Lemaire, L., Jacobi fields along harmonic 2-spheres in CP2 are integrable. J. London Math. Soc. (2) 66(2002), no. 2, 468486. http://dx.doi.org/10.1112/S0024610702003496
[P] Parker, T. H., Bubble tree convergence for harmonic maps. J. Differential Geom. 44(1996), no. 3, 595633.
[PW] Parker, T. H. and G.Wolfson, J., Pseudoholomorphic maps and bubble trees. J. Geom. Anal. 3(1993), no. 1, 6398. http://dx.doi.org/10.1007/BF02921330
[W] G.Wolfson, J., Harmonic sequences and harmonic maps of surfaces into complex Grassmann manifolds. J. Differential Geom. 27(1988), no. 1, 161178.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed