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$𝑆𝑒𝑐𝑜𝑛𝑑 - 𝑜𝑟𝑑𝑒𝑟𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝐿𝑜𝑟𝑒𝑛𝑡𝑧𝑖𝑎𝑛𝑠𝑝𝑎𝑐𝑒𝑠$ , that is to say, Lorentzian manifolds with vanishing second derivative $\nabla \nabla R \equiv 0$ of the curvature tensor $R$ , are characterized by several geometric properties, and explicitly presented. Locally, they are a product $M = M_{1} \times M_{2}$ 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., $\nabla R \neq 0$ at some point), the curvature tensor turns out to...

Submanifold geometry and Hessians on the pseudoriemannian manifold of metrics.

Neuwirther, M. (1993)

Acta Mathematica Universitatis Comenianae. New Series

Submanifolds of a Lorentzian para-Sasakian manifold.

De, U.C., Al-Aqeel, Adnan, Shaikh, A.A. (2005)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Supersymmetries-mathematics of supergeometry

K. Gawedzki (1977)

Annales de l'I.H.P. Physique théorique

Sur la détermination, par des données de Cauchy, des champs de Killing admis par un espace-temps

Bartolomé Coll (1976)

Annales de l'I.H.P. Physique théorique

Sur le théorème de Gauss-Bonnet pour les pseudo-métriques singulières

Fernand Pelletier (1986/1987)

Séminaire de théorie spectrale et géométrie

Sur l’holonomie des variétés pseudo-riemanniennes de signature $(n, n)$

L.Bérard Bergery, A. Ikemakhen (1997)

Bulletin de la Société Mathématique de France

Sur l'holonomie des variétés pseudo-riemanniennes de signature (2,2+n).

A. Ikemakhen (1999)

Publicacions Matemàtiques

In this paper, we determine a class of possible restricted holonomy groups for a non-irreducible indecomposable pseudoriemannian manifold with signature (2,2 + n). In particular, we deduce that which associated to symmetric spaces; and give some examples of such spaces. Finally, we construct some examples of metrics whose restricted holonomy groups are not closed.

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Spacelike Salkowski and anti-Salkowski curves with a spacelike principal normal in Minkowski 3-space.

Space-like surfaces in an anti-de Sitter space

Space-time distributions.

Space-times admitting a covariantly constant spinor field

Spinors on $C P^{2}$ in $d \geq 9$ supergravity

Stabilité par déformation non-linéaire de la métrique de Minkowski

Stable Minimal Surfaces and Spatial Topology in General Relativity.

Stable space-like hypersurfaces in the de Sitter space

Stable space-like hypersurfaces with constant scalar curvature in generalized Roberston-Walker spacetimes.

Structure of second-order symmetric Lorentzian manifolds