A Hamiltonian framework for 2+1 dimensional gravity coupled with matter (satisfying positive energy conditions) is considered in the asymptotically flat context. It is shown that the total energy of the system is non-negative, vanishing if and only if space-time is (globally) Minkowskian. Furthermore, contrary to one’s experience with usual field theories, the Hamiltonian is bounded from above....

Let M be a real hypersurface of complex space form n ( c ) $M^n(c)$ , ≠ 0 $c\ne 0$ . Suppose that the structure vector field ξ is an eigen Ricci tensor S, S = β $S\xi =\beta \xi$ being function. We study on M, gradient pseudo-Ricci soliton g f λ μ $M,g,f,\lambda ,\mu$ extended concept soliton, closely related to pseudo-Einstein hypersurfaces. When ≥ 3 $n\ge 3$ we show Hopf hypersurface.

For a variety of diffeomorphism–invariant field theories describing hypersurface motions (such as relativistic M -branes in space-time dimension M + 2) we perform a Hamiltonian reduction “at level 0”, showing that a simple algebraic function of the normal velocity is canonically conjugate to the shape Σ of the hypersurface. The Hamiltonian dependence on Σ is solely via the domain of integration...

Reflections from hypersurfaces act by symplectomorphisms on the space of oriented lines with respect to canonical symplectic form. We consider an arbitrary C?-smooth hypersurface ? ? ?n+1 that is either a global strictly convex closed hypersurface, or germ hypersurface. deal pseudogroup generated compositional ratios reflections and its small deformations. In case when we show C?-closure latter...

Abstract. Let X ⊂ Pr be a smooth algebraic curve in projective space, over an algebraically closed field of characteristic zero. For each m ∈ N, the m-flexes of X are defined as the points where the osculating hypersurface of degree m has higher contact than expected, and a hypersurface H ⊂ Pr is called a m-Hessian if it cuts X along its m-flexes. When X is a complete intersection, we give an e...

In a metric g.f.f -manifold we study lightlike hypersurfaces M tangent to the characteristic vector fields, and owing to the presence of the f -structure, we determine some decompositions of TM and of a chosen screen distribution obtaining two distributions invariant with respect to the structure. We discuss the existence of a g.f.f -structure on a lightlike hypersurface and, under suitable hyp...

In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on hypersurface in projective space.

We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y admitting a full exceptional sequence. Applications include the case in which X is Calabi-Yau and either X is a hypersurface in Y (this extends a previous result b...

Assume that there exists a hypersurface singularity which cannot be resolved by iterated monoidal transformations in positive characteristic. We show that in the set of defining functions of hypersurface singularities which cannot be resolved, we can find a function satisfying very strong conditions. By these conditions we may be able to deduce a contradiction under the above assumption. Beside...