ISOMETRIC IMMERSION OF MINIMAL SPHERICAL SUBMANIFOLD VIA THE SECOND STANDARD IMMERSION OF THE SPHERE

Let $M^n$ be a $n$-dimensional compact connected minimal submanifold of the unit sphere $S^{n+p}(1)$. In this paper we study the isometric immersion of $M^n$ into $SM(n +p + 1)$ via the second standard immersion of $S^{n+p}(1)$. We obtain some integral inequalities m terms of the spectrum of the Laplace operator of $M^n$ and find some restrictions on such immersions.