An inclusive immersion into a quaternionic manifold and its invariants (Q1679203)

The author studies inclusive surfaces in quaternionic manifolds using a quaternionic invariant \(\mathcal W_Q\) corresponding to the Willmore functional. He shows that \(\mathcal W_Q\) is independent of the choice of a quaternionic connection. Moreover, he establishes a lower bound for the invariant \(\mathcal W_Q\) and shows that equality holds if and only if the inclusive immersion is twistor holomorphic. The author also considers quaternionic Willmore immersions, i.e., stationary inclusive immersions of the functional \(\mathcal W_Q\). He shows that compact inclusive minimal surfaces either in a quaternionic Kähler manifold of dimension greater than four or in an anti-self-dual Einstein 4-manifold are quaternionic Willmore.