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Structure of second-order symmetric Lorentzian manifolds

Oihane F. Blanco, Miguel Sánchez, José M. Senovilla (2013)

Journal of the European Mathematical Society

𝑆𝑒𝑐𝑜𝑛𝑑 - 𝑜𝑟𝑑𝑒𝑟𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝐿𝑜𝑟𝑒𝑛𝑡𝑧𝑖𝑎𝑛𝑠𝑝𝑎𝑐𝑒𝑠 , that is to say, Lorentzian manifolds with vanishing second derivative R 0 of the curvature tensor R , are characterized by several geometric properties, and explicitly presented. Locally, they are a product M = M 1 × M 2 where each factor is uniquely determined as follows: M 2 is a Riemannian symmetric space and M 1 is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen–Wallach family. In the proper case (i.e., R 0 at some point), the curvature tensor turns out to...

Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

Ioffe, Alexander, Penot, Jean-Paul (1996)

Serdica Mathematical Journal

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented...

Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations

Alexandru Kristály, Vicenţiu Rădulescu (2009)

Studia Mathematica

Let (M,g) be a compact Riemannian manifold without boundary, with dim M ≥ 3, and f: ℝ → ℝ a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem - Δ g ω + α ( σ ) ω = K ̃ ( λ , σ ) f ( ω ) , σ ∈ M, ω ∈ H₁²(M), is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the function K̃. Here, Δ g stands for the Laplace-Beltrami operator on (M,g), and α, K̃ are smooth positive functions. These multiplicity...

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