Abstract:

The authors studied the spactral geometry of quasitotally real minimal submanifolds in a complex projective space. By means of the method of moving frames and caculating Laplacian of the mean curvature vector, the eigenvalue inequality for the submanifolds which only related to intrinsic geometric quality was established. This result generated correlation theorms to generic submanifolds in a complex projective space. Moreover, the authors also got one necessary and sufficient condition on uorder immersion of quasitotally real minimal submanifolds.

Key words: complex projective space, quasitotally real, minimal submanifolds, spactral geometry, eigenvalue inequalities