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...

We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metric...

In this paper, the reduction of biharmonic map equation in terms of the Maurer-Cartan form for all smooth map of an arbitrary compact Riemannian manifold into a compact Lie group (G, h) with bi-invariant Riemannian metric h is obtained. By this formula, all biharmonic curves into compaqct Lie groups are determined, and all the biharmonic maps of an open domain of R with the conformal metric of ...

We obtain KSS, Strichartz and certain weighted Strichartz estimates for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metri...

Very recently, Jleli and Samet [53] and Samet et. al. [52] reported that some fixed point result in G-metric spaces can be derived from the fixed point theorems in the setting of usual metric space. In this paper, we prove the existence and uniqueness of fixed points of certain cyclic mappings in the context of G-metric spaces that can not be obtained by usual fixed point results via techniques...

Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian $$(M=G/H,g)$$ whose geodesics orbits of one-parameter subgroups G. The corresponding metric g is called a geodesic metric. We study the form (G/H, g), such that G one compact classical Lie groups $${{\,\mathrm{SO}\,}}(n)$$ , $$\mathrm{U}(n)$$ and H diagonally embedded product $$H_1\times \cdots \times H_s$$ where...