Totally real minimal submanifolds in a quaternion projective space (Q5906761)

Let \(QP^n(c)\) be a \(4n\)-dimensional quaternionic projective space with constant quaternionic sectional curvature \(c>0\). In this paper, the author studies totally real minimal submanifolds in \(QP^n(c)\) and obtains the following result. Let \(M\) be a 4-dimensional compact oriented projectively flat totally real minimal submanifold in \(QP^4(c)\). If \(M\) has nonnegative Euler number and scalar curvature \(\rho>0\), then \(M\) is totally geodesic. However, it should be noticed that a projectively flat manifold is of constant sectional curvature. So, the above result may perhaps be trivial.