It turns out that if a reductive complement m of a homogeneous reductive space G/H possesses a number of properties (including its decomposability into an orthogonal sum of three Ad(H)-invariant irreducible subspaces) then there exists a simple way of determining whether an f -structure F on this space belongs to the classes G1f , NKf and Kill f of generalized Hermitian geometry with respect to...

It has recently been shown that a Hagedorn phase of string gas cosmology can provide a causal mechanism for generating a nearly scale-invariant spectrum of scalar metric fluctuations, without the need for an intervening period of de Sitter expansion. In this Letter, we compute the spectrum of tensor metric fluctuations (gravitational waves) in this scenario and show that it is also nearly scale...

Given compact Lie groups H ⊂ G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K maintains nonnegative curvature on G/H . Such an enlarging is possible if (K, H) is a symmetric pair, which yields many new examples of nonnegatively curved homogeneo...

A theorem of J. Hersch (1970) states that for any smooth metric on S, with total area equal to 4π, the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard S-action on S, one can restrict the Laplace operator to the subspace of S-invariant functions and consi...

Abstract. A real Bott manifold is the total space of iterated RP 1 bundles starting with a point, where each RP 1 bundle is projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their cohomology rings with Z/2 coefficients are isomorphic. A real Bott manifold is a real toric manifold and admits a flat riemannian metric invariant u...

We establish results on invariant approximation for fuzzy nonexpansive mappings defined on fuzzy metric spaces. As an application a result on the best approximation as a fixed point in a fuzzy normed space is obtained. We also define the strictly convex fuzzy normed space and obtain a necessary condition for the set of all t-best approximations to contain a fixed point of arbitrary mappings. A ...

We design a new McEliece-like rank metric based encryption scheme from Gabidulin codes. We explain why it is not affected by the invariant subspace attacks also known as Overbeck’s attacks. The idea of the design mixes two existing approaches designing rank metric based encryption schemes. For a given security our public-keys are more compact than for the same security in the Hamming metric bas...

In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to rotation, reflection, translation and scaling. A well-defined metric is then proposed on the associated feature space. We show the continuity of this metric. Som...

A criterion in terms of differential invariants for a metric on a surface to be Liouville is established. Moreover, in this paper we completely solve in invariant terms the local mobility problem of a 2D metric, considered by Darboux: How many quadratic in momenta integrals does the geodesic flow of a given metric possess? The method is also applied to recognition of other polynomial integrals ...

We present an explicit description of the Wu metric on the convex Thullen domains which turns out to be the first natural example of a purely Hermitian, non-Kählerian invariant metric. Also, we show that the Wu metric on these Thullen domains is in fact real analytic everywhere except along a lower dimensional subvariety, and is C1 smooth overall. Finally, we show that the holomorphic curvature...