In this note, we announce some results showing unexpected similarities between the moduli spaces of constant curvature metrics on 2-manifolds (the Riemann moduli space) and moduli spaces of Einstein metrics on 4manifolds. Let J? denote the moduli space of Einstein metrics of volume 1 on a compact, orientable 4-manifold M. If J£\ denotes the space of smooth Riemannian metrics of volume 1 on M, e...

Array codes or two-dimensional codes in m-metric are subsets/subspaces of the space Matm×s(Fq), the linear space of all m × s-matrices with entries from a finite field Fq endowed with the m-metric [15]. In this paper, we obtain a lower bound over the number of parity checks of a two-dimensional m-code that corrects any two-dimensional array which has both clustered errors as well as errors in s...

a cartan manifold is a smooth manifold m whose slit cotangent bundle 0t *m is endowed with a regularhamiltonian k which is positively homogeneous of degree 2 in momenta. the hamiltonian k defines a (pseudo)-riemannian metric ij g in the vertical bundle over 0 t *m and using it, a sasaki type metric on 0 t *m is constructed. a natural almost complex structure is also defined by k on 0 t *m in su...

The terminology and notation used here have been introduced in the following articles: [9], [4], [13], [12], [10], [8], [2], [3], [1], [14], [7], [11], [5], and [6]. Let M be a metric structure, and let x, y be elements of the carrier of M . The predicate x ≈ y is defined by: (Def.1) ρ(x, y) = 0. Let M be a metric structure, and let x be an element of the carrier of M . The functor x yielding a...

An M-space is a metric space (X, d) having the property that for each pair of points p, q ∈ X with d(p, q) = λ and for each real number α ∈ [0, λ], there is a unique rα ∈ X such that d(p, rα) = α and d(rα, q) = λ − α. In an M-space (X, d), we say that metric segments have unique prolongations if points p, q, r, s satisfy d(p, q) + d(q, r) = d(p, r), d(p, q) + d(q, s) = d(p, s) and d(q, r) = d(q...

On a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is invariant under the action of the diffeomorphism group, is a multiple of the Fisher–Rao metric. Introduction. The Fisher–Rao metric on the space Prob(M) of probability densities is of importance in the field of information geometry. Restricted to...

In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the qu...

We present a radically new indexing approach for approximate string matching. The scheme uses the metric properties of the edit distance and can be applied to any other metric between strings. We build a metric space where the sites are the nodes of the suffix tree of the text, and the approximate query is seen as a proximity query on that metric space. This permits us finding the occ occurrenc...

A projective algebraic manifold M is a complex manifold in certain projective space CPm, m ≥ dimC M = n. The hyperplane line bundle of CPm restricts to an ample line bundle L onM . The bundle is a polarization onM . Suppose g is a Kähler metric on M . We say g is a polarized Kähler metric with respect to L, if the corresponding Kähler form represents the first Chern class c1(L) of L in H 2(M,Z)...

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.