A rectangular rod is placed in a flow field flowing parallel to a flat plate. Effect of chord-thickness ratio of rectangular rod on developing vortex shedding downstream to the rod is studied. Then, for each one of the aspect ratios, the distance of the rod from the neighboring flat plate is reduced until the rod sticks to the flat plate. In each case, the effect of the flat plate boundary laye...

The classical knot groups are the fundamental groups of the complements of smooth or piecewise-linear (PL) locally-flat knots. For PL knots that are not locally-flat, there is a pair of interesting groups to study: the fundamental group of the knot complement and that of the complement of the “boundary knot” that occurs around the singular set, the set of points at which the embedding is not lo...

We obtain an Einstein metric of constant negative curvature given an arbitrary boundary metric in three dimensions, and a conformally flat one given an arbitrary conformally flat boundary metric in other dimensions. In order to compute the on-shell value of the gravitational action for these solutions, we propose to integrate the radial coordinate from the boundary till a critical value where t...

We study the semi-Riemannian geometry of foliation F an indefinite locally conformal Kähler (l.c.K.) manifold M, given by Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is Lee form M). If M conformally flat then every leaf shown to be a totally geodesic hypersurface in space sectional curvature c/4, carrying c-Sasakian structure. As corollary result together with version de Rham decom...

A rectangular rod is placed in a flow field flowing parallel to a flat plate. Effect of chord-thickness ratio of rectangular rod on developing vortex shedding downstream to the rod is studied. Then, for each one of the aspect ratios, the distance of the rod from the neighboring flat plate is reduced until the rod sticks to the flat plate. In each case, the effect of the flat plate boundary laye...

We show that the moduli space of deformations of a compact coassociative submanifold L has a natural local embedding as a submanifold of H(L,R). We show that a G2-manifold with a T -action of isomorphisms such that the orbits are coassociative tori is locally equivalent to a minimal 3-manifold in R with positive induced metric where R ∼= H(T ,R). By studying minimal surfaces in quadrics we show...

The main result of this paper is that a Lorentzian manifold is locally conformally equivalent to a manifold with recurrent lightlike vector field and totally isotropic Ricci tensor if and only if its conformal tractor holonomy admits a 2-dimensional totally isotropic invariant subspace. Furthermore, for semi-Riemannian manifolds of arbitrary signature we prove that the conformal holonomy algebr...

We prove that every Kähler metric, whose potential is a function of the timelike distance in the flat Kähler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kähler manifolds with the above mentioned metrics. New examples of Sasakian space forms are obtained as real hypersurfaces of a Kähler space form ...