Willmore totally real submanifolds of complex space forms \(\tilde M^{n+p}(4c)\). (English) Zbl 1513.53112
Summary: Let \(M\) be an \(n\)-dimensional compact Willmore totally real submanifold of complex space forms \(\tilde M^{n+p}(4c),(p > 0)\). In this paper, we obtain some integral inequalities of Simons’ type and characterization theorems of \(n\)-dimensional compact Willmore totally real submanifolds of \(\tilde M^{n+p}(4c)\), which are connected with the squared norm of the second fundamental form and the mean curvature as well as the sectional curvature and Ricci curvature of \(M\).
MSC:
53C40 | Global submanifolds |
53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
53B25 | Local submanifolds |
32V40 | Real submanifolds in complex manifolds |