TOTAL CURVATURE OF PSEUDO-UMBILICAL SURFACE

摘要

It is a well-known fact that the total curvature of a minimal surface in the Euclidean space E^n is equal to the negative of the volume of its image under the Gaussian map. Recently, Professor Chen Zhihua established similar results for the minimal surfaces in sphere S^n and pseudo-sphere H^n respectively (Kexue Tongbao, 31(1986), 12: 793—797). Let M be a surface of an n-dimensional