We are concerned with super-Liouville equations on the two sphere, which have variational structure a strongly-indefinite functional. prove existence of non-trivial solutions by combining use Nehari manifolds, balancing conditions and bifurcation theory.

We study null hypersurfaces of indefinite Kähler manifolds and by taking the advantages almost complex structure $J$, we select a suitable rigging $\zeta$, which call $J-$rigging, on hypersurface. This enables us to build an associated Hermitian metric $\breve{g}$ ambient space is restricted into non-degenerated $\widetilde{g}$ normalized derive Gauss-Weingarten type formulae for hypersurface $...