Isometric Surfaces and the Third Laplace-Beltrami

Abstract

In this paper, classical isometric helicoidal and rotational surfaces are studied, and generalized by Bour's theorem in three dimensional Euclidean space. Moreover, the third Laplace-Beltrami operators of two classical surfaces are obtained.

arXiv comment7 pages, 2 figures This paper has been withdrawn by the author due to a crucial error in some equations