G2-Monopoles with Singularities (Examples)

© 2016 Springer Science+Business Media DordrechtG2-Monopoles are solutions to gauge theoretical equations on G2-manifolds. If the G2-manifolds under consideration are compact, then any irreducible G2-monopole must have singularities. It is then important to understand which kind of singularities G2-monopoles can have. We give examples (in the noncompact case) of non-Abelian monopoles with Dirac type singularities, and examples of monopoles whose singularities are not of that type. We also give an existence result for Abelian monopoles with Dirac type singularities on compact manifolds. This should be one of the building blocks in a gluing construction aimed at constructing non-Abelian ones.

Some examples of special Lagrangian tori

A short paper giving some examples of smooth hypersurfaces M of degree n+1 in complex projective n-space that are defined by real polynomial equations and whose real slice contains a component diffeomorphic to an n-1 torus, which is then special Lagrangian with respect to the Calabi-Yau metric on M.