| Popis: |
We study a kind of complex submanifolds in a quaternion projective space \(\mathbb {H}P^n\), which we call transversally complex submanifolds, from the viewpoint of quaternionic differential geometry. There are several examples of transversally complex immersions of Hermitian symmetric spaces. For a transversally complex immersion \(f:M\rightarrow \mathbb {H}P^n \), a key notion is a Gauss map associated with f, which is a map \(S:M \rightarrow \mathrm{End}(\mathbb {H}^{n+1})\) with \(S^2 = -\mathrm{id}\). Our theory is an attempt of a generalization of the theory “Conformal geometry of surfaces in \(S^4\) and quaternions” by Burstall, Ferus, Leschke, Pedit, and Pinkall [4]. |
