Turkish Journal of Mathematics
Abstract
An immersion \phi colon M to \tilde M^2 of a surface M into a Kaehler surface is called purely real if the complex structure J on \tilde M^2 carries the tangent bundle of M into a transversal bundle. In the first part of this article, we prove that the equation of Ricci is a consequence of the equations of Gauss and Codazzi for purely real surfaces in any Kaehler surface. In the second part, we obtain a necessary condition for a purely real surface in a complex space form to be minimal. Several applications of this condition are provided. In the last part, we establish a general optimal inequality for purely real surfaces in complex space forms. We also obtain three classification theorems for purely real surfaces in C^2 which satisfy the equality case of the inequality.
DOI
10.3906/mat-0809-44
Keywords
Purely real surfaces; integrability condition; equation of Ricci; equation of Gauss-Codazzi; Kaehler surface; Wirtinger angle; optimal inequality.
First Page
275
Last Page
292
Recommended Citation
CHEN, B (2010). On purely real surfaces in Kaehler surfaces. Turkish Journal of Mathematics 34 (2): 275-292. https://doi.org/10.3906/mat-0809-44
