We give a construction to obtain canonically an “isotropic average” of given C-close isotropic submanifolds of a symplectic manifold. To do so we use an improvement of Weinstein’s submanifold averaging theorem (obtained in collaboration with H. Karcher) and apply “Moser’s trick”. We also present an application to Hamiltonian group actions.

We discuss the (causal) structure of a recently found black hole solution of eompactffied d = 11 supergravity. It is shown that the singularity is in fact lightlike and coincides with the horizon. Consequences are that the Hawking temperature is undetermined and that there is no other universe connected to the singularity. In a previous paper in collaboration with P. van Nieuwenhuizen [ 1 ], we...

We study some properties of a half-lightlike submanifoldM , of a semi-Riemannianmanifold, whose shape operator is conformal to the shape operator of its screen distribution. We show that any screen distribution S(TM) of M is integrable and the geometry of M has a close relation with the nondegenerate geometry of a leaf of S(TM). We prove some results on symmetric induced Ricci tensor and null s...

We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant submanifolds in the form N N⊥×fNT by reversing two factor manifolds NT and N⊥. W...

We study GCR-lightlike submanifolds of semi-Riemannian product manifolds. give some equivalent conditions for the integrability various distributions manifolds and investigate geometry leaves distributions.