A class of generalized special Weingarten surfaces

Autor:	Carlos M. C. Riveros, Armando M. V. Corro, Diogo G. Dias
Rok vydání:	2019
Předmět:	Class (set theory) Pure mathematics General Mathematics 010102 general mathematics 0103 physical sciences Euclidean geometry 010307 mathematical physics 0101 mathematics GEOM 01 natural sciences Mathematics
Zdroj:	International Journal of Mathematics. 30:1950075
ISSN:	1793-6519 0129-167X
DOI:	10.1142/s0129167x19500757
Popis:	In [Classes of generalized Weingarten surfaces in the Euclidean 3-space, Adv. Geom. 16(1) (2016) 45–55], the authors study a class of generalized special Weingarten surfaces, where coefficients are functions that depend on the support function and the distance function from a fixed point (in short EDSGW-surfaces), this class of surfaces has the geometric property that all the middle spheres pass through a fixed point. In this paper, we present a Weierstrass type representation for EDSGW-surfaces with prescribed Gauss map which depends on two holomorphic functions. Also, we classify isothermic EDSGW-surfaces with respect to the third fundamental form parametrized by planar lines of curvature. Moreover, we give explicit examples of EDSGW-surfaces and isothermic EDSGW-surfaces.
Databáze:	OpenAIRE
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