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Manifolds with special structures are presently actively investigated by mathematicians and physicists. They are related to outstanding theoretical questions in geometry and appear as models in the string theory. Our aims are: 1. Finding necessary and sufficient conditions for the existence of a closed G2-structure (resp. a flat G2-structure among a given cohomology class) on a 7-manifold. 2. Finding global invariants of closed G2-structures. 3. Investigating the above problems for multi-symplectic forms in dimensions 6 and 8. 4. Finding necesary and sufficient conditions for the existence of symplectic or Kaehler submanifolds realizing a given homology class. 5. Develop techniques to deal with above problems in a general framework. Our main approach to this project has been guided by recent observations that it is not only possible to apply methods presently known. It must be here a bigger framework which unifies these problems and these methods.
Main investigator:
IM team members:
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Vanžura Jiří |
Participating institutions:
Institute of Mathematics, AS CR
