The first Chern class and conformal area for a twistor holomorphic immersion

• Hasegawa, Kazuyuki

Abstract

We obtain an inequality involving the first Chern class of the normal bundle and the conformal area for a twistor holomorphic surface. Using this inequality, we can improve an inequality obtained by T. Friedrich for the Euler class of the normal bundle of a twistor holomorphic surface in the four-dimensional space form. Moreover, as a corollary, we see that the area of a superminimal surface in the unit sphere is an integer multiple of {Mathematical expression}, which is essentially proved by E. Calabi. © 2014 Mathematisches Seminar der Universität Hamburg and Springer-Verlag Berlin Heidelberg.

in Press

Journal

• Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

  Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 84 (1), 67-83, 2014-01-01

  Mathematisches Seminar der Universität Hamburg / Springer-Verlag

Keywords

• Conformal area
• First Chern class
• Twistor holomorphic surface
• Twistor lift

Details

• CRID: 1050564285878260608
• NII Article ID: 120005418472
• NII Book ID: AA00504553
• ISSN: 00255858
• ISSN: 18658784
• DOI: 10.1007/s12188-014-0089-3
• Web Site: http://hdl.handle.net/2297/36984
• Web Site: http://link.springer.com/content/pdf/10.1007/s12188-014-0089-3.pdf
• Web Site: http://link.springer.com/article/10.1007/s12188-014-0089-3/fulltext.html
• Web Site: http://link.springer.com/content/pdf/10.1007/s12188-014-0089-3
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
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  • CiNii Articles
  • KAKEN