Hi all,

Let $M$ be a real-analytic manifold and let $N$ be a complexification of $M$ (in other words, $M$ sits in $N$ as a totally real submanifold). Suppose $M$ has an (integrable) complex structure. Does it extend in a neighborhood of $M$ in $N$ (in a unique "natural" way?) such that $N$ becomes a manifold with a quaternionic structure? (If not, what additional data/restrictions are required?)

What if $M$ has a real-analytic Kahler structure? Does it extend in N as a hyperkahler structure? If so, what does this have to do with the hyperkahler structure in (a neighborhood of the zero section in) the holomorphic cotangent bundle of $M$ described by Feix and Kaledin?

Thanks in advance for your insights.

Your Answer

 
discard

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.