Let X = G/P be a homogeneous space of a complex semisimple Lie group G equipped with a hermitian metric. We study the action of the Hodge star operator on the space of harmonic differential forms on X. We obtain explicit combinatorial formulas for this action when X is an irreducible hermitian symmetric space of compact type.

In this paper, we study left-invariant Einstein-like metrics on the compact Lie group G. Assume that there exist two subgroups, H⊂K⊂G, such G/K is a compact, connected, irreducible, symmetric space, and isotropy representation of G/H has exactly inequivalent, irreducible summands. We prove left metric ⟨·,·⟩t1,t2 G defined by first equation, must be an A-metric. Moreover, groups do not admit non...

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-m...

A classical question in the theory of functional equations is the following: “When is it true that a function which approximately satisfies a functional equation E must be close to an exact solution of E?” If the problem accepts a solution, we say that the equation E is stable. The first stability problem concerning group homomorphisms was raised by Ulam [30] in 1940. We are given a group G and...

The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate. By associating to an instanton its energy density, we can examine the information metric g on the moduli spaces M of self-dual connections over Riemannian 4-manifolds. Compared with the more widely ...

This paper is connected with the problem of describing path metric spaces which are homeomorphic to manifolds and biLipschitz homogeneous, i.e., whose biLipschitz homeomorphism group acts transitively. Our main result is the following. LetX = G/H be a homogeneous space of a Lie group G, and let d be a geodesic distance on X inducing the same topology. Suppose there exists a subgroup GS of G whi...

This paper presents a distributed algorithm that runs on an n-node unit ball graph (UBG) G residing in a metric space of constant doubling dimension, and constructs, for any ε > 0, a (1 + ε)-spanner H of G with maximum degree bounded above by a constant. In addition, we show that H is “lightweight”, in the following sense. Let ∆ denote the aspect ratio of G, that is, the ratio of the length of ...

We compute the hessian iddW of the natural metric form W on the twistor space T(M, g) of a 4-dimensional Riemannian manifold (M, g). We then adapt the computations to the case of the twistor space T(M, g,D) of a hyperkähler manifold (M, g,D = (I, J,K)). We show a strong positivity property of the hessian iddW on the twistor space T(M, g,D) and prove, as an application, a convexity property of t...

Let G be a Lie group, G its Lie algebra, T G its cotangent bundle and D := tG the Lie algebra of T G. We investigate the group of automorphisms of D. More precisely, we fully characterize the space of all derivations of D. As a byproduct, we also characterize some spaces of operators on G amongst which the space J of bi-invariant tensors on G and prove that if G has a bi-invariant Riemannian or...