Let M be an n-dimensional compact minimal submanifold in a Riemannian manifold V+

of quasi constant curvature

Let K and Q be the infinimum of the Sectional curvature and Ricci Curvature of M respectively. Let R be the Scalar curvature of M

in this paper

we obtain some relations of K

Q and R

give some sufficient conditions for a compact minimal submanifold in Vn+p to be totally geodesic submanifold. In particular

when Vn+p is a manifold of constant curvature. i. e. b= 0

we obtain the same result of S. T. Yau's Theorem.