In this paper we study the lower semicontinuous envelope with respect to the L-topology of a class of isotropic functionals with linear growth defined on mappings from the n-dimensional ball into RN that are constrained to take values into a smooth submanifold Y of RN . Let B be the unit ball in R and Y a smooth Riemannian manifold of dimension M ≥ 1, isometrically embedded in R for some N ≥ 2....

A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. The Weyl surface describing the dependence of Green’s matrix on the boundary conditions is interpreted as the set of maximally isotropic subspace of a quadratic from given by the Wronskian. Analysis of the possibly degenerate limit quadratic form leads to the limit point/l...

We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the boundary. We show that one can recover uniquely a conformal factor near a strictly convex point where we have the information. In particular, this implies that we c...

Our topological setting is a smooth compact manifold of dimension two or higher with boundary. Although this underlying structure smooth, the Riemannian metric tensor only assumed to be bounded and measurable. This known as rough manifold. For large class boundary conditions we demonstrate Weyl law for asymptotics eigenvalues Laplacian associated metric. Moreover, obtain eigenvalue weighted Lap...

Motivated by the invariance of current representations of quantum gravity under diffeomorphisms much more general than isometries, the Haag-Kastler setting is extended to manifolds without metric background structure. First, the causal structure on a differentiable manifold M of arbitrary dimension (d+1 > 2) can be defined in purely topological terms, via cones (C-causality). Then, the general ...

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...

We obtain an algorithm computing the Chern-Schwartz-MacPherson (CSM) classes of Schubert cells in a generalized flag manifold G{B. In analogy to how the ordinary divided difference operators act on Schubert classes, each CSM class of a Schubert class is obtained by applying certain Demazure-Lusztig type operators to the CSM class of a cell of dimension one less. These operators define a represe...

A compact quasi-regular Sasakian manifold M is foliated by onedimensional leaves and the transverse space of this characteristic foliation is necessarily a compact Kähler orbifold Z. In the case when the transverse space Z is also Einstein the corresponding Sasakian manifold M is said to be Sasakian η-Einstein. In this article we study η-Einstein geometry as a class of distinguished Riemannian ...

The existence of a new kind of branes for the open topological A-model is argued by using the generalized complex geometry of Hitchin and the SYZ picture of mirror symmetry. Mirror symmetry suggests to consider a bi-vector in the normal direction of the brane and a new definition of generalized complex submanifold. Using this definition, it is shown that there exists generalized complex submani...

the objective of this work was to develop a new design of an intake manifold through a 1d simulation. it is quite familiar that a duly designed intake manifold is essential for the optimal performance of an internal combustion engine. air flow inside the intake manifold is one of the important factors, which governs the engine performance and emissions. hence the flow phenomenon inside the inta...