SPECIAL SURFACES IN R3
Abstract
The principal objects of this paper are regular parametrical surfaces in 
. The method we want to use is based on Weingarten mapping. We suppose that the mapping 
, where 
and 
, is regular. Symbols 
and 
are used in this paper instead of 
, 
etc. These vectors form the basis of tangent space 
(see Fig.1). On 
we can construct moving frame ( 
). Vectors and 
are tangent vector fields of 
, 
is a normal vector field and 
is a unit normal vector field. In this paper we are going to study Gauss and Mean curvature of some classical surfaces with methods based on Weingarten mapping
References
Bureš, J., Kaňka, M. “Some Conditions for a Surface in to be a Part of the Sphere ”. Mathematica Bohemica 4 1994. s. 367–371.
Cartan, É. Oeuvres complètes-Partie II Vol. 1. Paris: Gauthier-Villars, 1953.
Cartan, É. Oeuvres complètes-Partie II Vol. 2. Paris: Gauthier-Villars, 1953.
Kaňka, M. “Example of Basic Structure Equations of Riemannian Manifolds”, Mundus Symbolicus 3 1995. s. 57–62.
Chern, SS. “Some new Viewpoints in Differential geometry in the large.” Bulletin of the American mathematical Society. 1946: 1–30.
Kaňka, M., Kaňková, E. “Geometry of functions in Economics.” Research Journals of Economics, Business and ICT. 2011: 1–4. ISSN: 2045–3345.
Kaňka, M., Kaňková, E. “Some examples of production functions.” Research Journals of Economics, Business and ICT. 2011: 5–8. ISSN: 2045–3345.
Kobayashi, S., Nomizu, K. Foundations of Differential Geometry. New York: Wiley (Inter-science), 1963.
Kostant, B. “On differential geometry and homogeneous space. 1.” Proceedings of the national Academy of sciences of the United States of America. 1956: 258–261.
Kostant, B. “On differential geometry and homogeneous space. 2.” Proceedings of the national Academy of sciences of the United States of America. 1956: 354–357.
Nomizu, K. Lie Groups and Differential Geometry. Tokyo: The Mathematical Society of Japan, 1956.
Rauch, H. “A contribution to differential geometry in the large.” Annals of Mathematics. 1961:38–55.
Sternberg, S. Lectures on Differential Geometry. Englewood Cliffs, N.J.: Prentice-Hall, 1964.
Copyright information
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (Creative Commons Attribution License 3.0 - CC BY 3.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
