Previous |  Up |  Next


Title: A note on surfaces with radially symmetric nonpositive Gaussian curvature (English)
Author: Shomberg, Joseph
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 130
Issue: 2
Year: 2005
Pages: 167-176
Summary lang: English
Category: math
Summary: It is easily seen that the graphs of harmonic conjugate functions (the real and imaginary parts of a holomorphic function) have the same nonpositive Gaussian curvature. The converse to this statement is not as simple. Given two graphs with the same nonpositive Gaussian curvature, when can we conclude that the functions generating their graphs are harmonic? In this paper, we show that given a graph with radially symmetric nonpositive Gaussian curvature in a certain form, there are (up to) four families of harmonic functions whose graphs have this curvature. Moreover, the graphs obtained from these functions are not isometric in general. (English)
Keyword: Gaussian curvature
Keyword: holomorphic function
MSC: 35C05
MSC: 53A05
idZBL: Zbl 1108.53004
idMR: MR2148650
DOI: 10.21136/MB.2005.134135
Date available: 2009-09-24T22:19:45Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] Conway, J. B.: Functions of One Complex Variable I.Second edition. Springer, New York, 1973. MR 0447532
Reference: [2] Millman, R. S., Parker, G. D.: Elements of Differential Geometry.Prentice-Hall, New Jersey, 1977. MR 0442832
Reference: [3] Pressley, A.: Elementary Differential Geometry.Springer, London, 2001. Zbl 0959.53001, MR 1800436
Reference: [4] Weissteins’, E.: Mathworld.Wolfram Research, Inc. CRC Press LLC,, 1999.


Files Size Format View
MathBohem_130-2005-2_5.pdf 413.6Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo