Journal of Applied Mathematics

Some Surfaces with Zero Curvature in 2 ×

Dae Won Yoon

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Abstract

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

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

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305630

Digital Object Identifier
doi:10.1155/2014/154294

Mathematical Reviews number (MathSciNet)
MR3191105

Citation

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. https://projecteuclid.org/euclid.jam/1425305630


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References

  • 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