Journal of Applied Mathematics

Some Surfaces with Zero Curvature in 2 ×

Dae Won Yoon

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We study surfaces defined as graph of the function z = f ( x , y ) in the product space 2 × . In particular, we completely classify flat or minimal surfaces given by f ( x , y ) = u ( x ) + v ( y ) , where u ( x ) and v ( y ) are smooth functions.

Article information

J. Appl. Math., Volume 2014 (2014), Article ID 154294, 5 pages.

First available in Project Euclid: 2 March 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)


Yoon, Dae Won. Some Surfaces with Zero Curvature in ${\Bbb H}^{2}{\times}\Bbb R$. J. Appl. Math. 2014 (2014), Article ID 154294, 5 pages. doi:10.1155/2014/154294.

Export citation


  • J. Gegenberg, S. Vaidya, and J. F. Vázquez-Poritz, “Thurston geometries from eleven dimensions,” Classical and Quantum Gravity, vol. 19, no. 23, pp. L199–L204, 2002.
  • W. Thurston, Three-Dimensional Geometry and Topology, vol. 35 of Princeton Mathematical Series, Princeton University Press, Princeton, NJ, USA, 1997.
  • J. M. Espinar, M. M. Rodríguez, and H. Rosenberg, “The extrinsic curvature of entire minimal graphs in ${H}^{2}\times R$,” Indiana University Mathematics Journal, vol. 59, no. 3, pp. 875–889, 2010.
  • I. Fernández and P. Mira, “Harmonic maps and constant mean curvature surfaces in ${H}^{2}\times R$,” The American Journal of Mathematics, vol. 129, no. 4, pp. 1145–1181, 2007.
  • Y. W. Kim, S. E. Koh, H. Shin, and S. D. Yang, “Helicoidal minimal surfaces in ${H}^{2}\times R$,” Bulletin of the Australian Mathematical Society, vol. 86, no. 1, pp. 135–149, 2012.
  • S. Montaldo and I. I. Onnis, “Invariant CMC surfaces in ${H}^{2}\times R$,” Glasgow Mathematical Journal, vol. 46, no. 2, pp. 311–321, 2004.
  • S. Montaldo and I. I. Onnis, “A note on surfaces in ${H}^{2}\times R$,” Bollettino della Unione Matematica Italiana B, vol. 10, no. 3, pp. 939–950, 2007.
  • B. Nelli and H. Rosenberg, “Minimal surfaces in ${H}^{2}\times R$,” Bulletin of the Brazilian Mathematical Society, vol. 33, no. 2, pp. 263–292, 2002.
  • D. W. Yoon, “Minimal translation surfaces in ${H}^{2}\times R$,” Taiwanese Journal of Mathematics, vol. 17, no. 5, pp. 1545–1556, 2013.
  • A. L. Albujer, “New examples of entire maximal graphs in ${H}^{2}\times {R}_{1}$,” Differential Geometry and its Applications, vol. 26, no. 4, pp. 456–462, 2008. \endinput