JOURNAL BROWSE
Search
Advanced SearchSearch Tips
SURFACES WITH PLANAR LINES OF CURVATURE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 32, Issue 4,  2010, pp.777-790
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2010.32.4.777
 Title & Authors
SURFACES WITH PLANAR LINES OF CURVATURE
Kim, Dong-Soo; Kim, Young-Ho;
  PDF(new window)
 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
lines of curvature;surface of revolution;slant cylinder;generalized slant cylinder;Weingarten surface;
 Language
English
 Cited by
1.
SURFACES WITH POINTWISE 1-TYPE GAUSS MAP,;

한국수학교육학회지시리즈B:순수및응용수학, 2011. vol.18. 4, pp.369-377 crossref(new window)
2.
SURFACES WITH POINTWISE 1-TYPE GAUSS MAP OF THE SECOND KIND,;

한국수학교육학회지시리즈B:순수및응용수학, 2012. vol.19. 3, pp.229-237 crossref(new window)
3.
ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES,;;

한국수학교육학회지시리즈B:순수및응용수학, 2013. vol.20. 3, pp.149-158 crossref(new window)
4.
RULED SURFACES AND GAUSS MAP,;

대한수학회보, 2015. vol.52. 5, pp.1661-1668 crossref(new window)
1.
SURFACES WITH POINTWISE 1-TYPE GAUSS MAP OF THE SECOND KIND, The Pure and Applied Mathematics, 2012, 19, 3, 229  crossref(new windwow)
2.
RULED SURFACES AND GAUSS MAP, Bulletin of the Korean Mathematical Society, 2015, 52, 5, 1661  crossref(new windwow)
3.
Cheng–Yau Operator and Gauss Map of Surfaces of Revolution, Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39, 4, 1319  crossref(new windwow)
4.
SURFACES WITH POINTWISE 1-TYPE GAUSS MAP, The Pure and Applied Mathematics, 2011, 18, 4, 369  crossref(new windwow)
5.
ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES, The Pure and Applied Mathematics, 2013, 20, 3, 149  crossref(new windwow)
 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.