Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

SURFACES WITH PLANAR LINES OF CURVATURE

  • Kim, Dong-Soo (Department of Mathematics, Chonnam National University) ;
  • Kim, Young-Ho (Department of Mathematics, Kyungpook National University)
  • Received : 2010.11.01
  • Accepted : 2010.12.09
  • Published : 2010.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

We study surfaces in the 3-dimensional Euclidean space with two family of planar lines of curvature. As a result, we establish some characterization theorems for such surfaces.

Keywords

References

  1. R. L. Bryant, Surfaces of mean curvature one in hyperbolic space, Theorie des varietes minimales et applications (Palaiseau, 1983-1984), Asterisque 154- 155(1987), 321-347.
  2. B. -Y. Chen, Geometry of submanifolds, Pure and Applied Mathematics, No. 22, Marcel Dekker Inc., New York, 1973.
  3. G. Darboux, Lecons sur la theorie generale des surfaces I, II, Editions Jacques Gabay, Sceaux, 1993.
  4. M. P. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Englewood Cliffs, NJ., 1976.
  5. H. Hopf, Uber Flachen mit einer Relation zwischen den Hauptkrummungen, Math. Nachr. 4(1951), 232-249.
  6. W. Klingenberg, A course in differential geometry, Springer-Verlag, New York Inc., 1983.
  7. W. Kuhnel, Differential geometry: curves-surfaces-manifolds, Student Mathe- matical Library, 16, Amer. Math. Soc., Providence, RI., 2002.
  8. J. C. C. Nitsche, Lectures on minimal surfaces. Vol. 1. Introduction, fundamen- tals, geometry and basic boundary value problems. Translated from the German by Jerry M. Feinberg, Cambridge University Press, Cambridge, 1989.
  9. B. O'Neill, Elementary differential geometry(2nd ed.), Academic Press, San Diego, CA., 1997.
  10. M. Spivak, A comprehensive introduction to differential geometry Vol. III, Pub- lish or Perish Inc., Wilmington, Del., 1979.

Cited by

  1. Cheng–Yau Operator and Gauss Map of Surfaces of Revolution vol.39, pp.4, 2016, https://doi.org/10.1007/s40840-015-0234-x
  2. ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES vol.20, pp.3, 2013, https://doi.org/10.7468/jksmeb.2013.20.3.149
  3. SURFACES WITH POINTWISE 1-TYPE GAUSS MAP vol.18, pp.4, 2011, https://doi.org/10.7468/jksmeb.2011.18.4.369
  4. SURFACES WITH POINTWISE 1-TYPE GAUSS MAP OF THE SECOND KIND vol.19, pp.3, 2012, https://doi.org/10.7468/jksmeb.2012.19.3.229
  5. RULED SURFACES AND GAUSS MAP vol.52, pp.5, 2015, https://doi.org/10.4134/BKMS.2015.52.5.1661