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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