In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an (ε...

Vibronic coupling within the excited electronic manifold of the solute all-trans-β-carotene through the vibrational motions of the solvent cyclohexane is shown to manifest as the "molecular near-field effect," in which the solvent hyper-Raman bands are subject to marked intensity enhancements under the presence of all-trans-β-carotene. The resonance hyper-Raman excitation profiles of the enhanc...

Full understanding of synchronous behavior in coupled dynamical systems beyond the identical case requires an explicit construction of the generalized synchronization manifold, whether we wish to compare the systems or to understand their stability. Nonetheless, while synchronization has become an extremely popular topic, the bulk of the research in this area has been focused on the identical c...

Based on Colombeau’s theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic properties, in particular with respect to some new point value concepts for generalized functions and indicate applications of the resulting theory in general rela...

We investigate Kaluza-Klein metrics with a recurrent lightlike vector field over a pseudo-Riemannian manifold (B, g).

Characteristic numbers of compact hyper-Kähler manifolds are expressed in graphtheoretical form, considering them as a special case of the curvature invariants introduced by L. Rozansky and E. Witten. The appropriate graphs are generated by “wheels,” and the recently proved Wheeling theorem is used to give a formula for the L 2-norm of the curvature of an irreducible hyper-Kähler manifold in te...

Abstract We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold, when the diffusion constant goes to zero. If the drift of the diffusion is given by a Morse-Smale vector field b, the limits of the eigenfunctions concentrate on the recurrent set of b. A blow-up analysis enables us to find the main properties of the limit...

Recently, L.Rozansky and E.Witten [RW] associated to any hyper-Kähler manifold X an invariant of topological 3-manifolds. In fact, their construction gives a system of weights c Γ (X) associated to 3-valent graphs Γ and the corresponding invariant of a 3-manifold Y is obtained as the sum c Γ (X)I Γ (Y) where I Γ (Y) is the standard integral of the product of linking forms. So the new ingredient...

Recently, L.Rozansky and E.Witten [RW] associated to any hyper-Kähler manifold X an invariant of topological 3-manifolds. In fact, their construction gives a system of weights c Γ (X) associated to 3-valent graphs Γ and the corresponding invariant of a 3-manifold Y is obtained as the sum c Γ (X)I Γ (Y) where I Γ (Y) is the standard integral of the product of linking forms. So the new ingredient...

Suppose M is a topological m-manifold, X is a generalized nmanifold satisfying the disjoint disks property (DDP ), m > n ≥ 5, f : M → X is an approximate fibration, with fiber the shape of a closed topological manifold F , and Y is a closed, 1-LCC, codimension three subset of X. We examine conditions under which f is controlled homeomorphic to an approximate fibration g : M → X such that g|g−1(...