Abstract:

We studied the totally real pseudoumbilical submanifolds in quasicomplex projective space by means of the method of moving frams. Based  on the Stokes theorem and the Lapalacian of the square of the length of the second fundamental form, an integral inequality and a instrinsic rigidity theorem were obtained, which makes the study of the totally real pseudoumbilical submanifolds extend from the complex projective to the quasicomplex projective.

Key words: quasicomplex projective space, totally real submanifold, pseudoumbilical submanifold, totally umbilical