We consider nonlinear hyperbolic conservation laws, posed on a differential (n + 1)-manifold with boundary referred to as a spacetime, and in which the “flux” is defined as a flux field of n-forms depending on a parameter (the unknown variable). We introduce a formulation of the initial and boundary value problem which is geometric in nature and is more natural than the vector field approach re...

In this paper, we study the intrinsic structures of high-dimensional data sets for analyzing their geometrical properties, where core message is hiding on some nonlinear manifolds. Using manifold learning technique with a particular focus mean curvature, develop new methods to investigate uniqueness constant curvature spacelike hypersurfaces in Lorentzian warped product Furthermore, extend stoc...

Abstract This paper constructs in the framework of algebraic quantum field theory (AQFT) linear Chern–Simons/Wess–Zumino–Witten system on a class 3-manifolds M whose boundary $$\partial M$$ ∂ M is endowed with Lorentzian metric. It proven that this AQFT equivalent to di...

Abstract We study the geometry of foliated non-Lorentzian spacetimes in terms Godbillon-Vey class foliation. relate intrinsic torsion a Aristotelian manifold to its class, and interpret it as measure local spin spatial leaves time direction. With this characterisation, is an obstruction integrability $\sfG$-structure defining spacetime. use these notions formulate new geometric approach hydrody...

This paper is a contribution to harmonic analysis of compact solvmanifolds. We consider the four-dimensional oscillator group ${\rm Osc}_1$, which semi-direct product three-dimensional Heisenberg and real line. classify lattices Osc}_1$ up inner automorphisms Osc}_1$. For every lattice $L$ in we compute decomposition right regular representation on $L^2(L\backslash{\rm Osc}_1)$ into irreducible...

We study inverse problems for the nonlinear wave equation □gu+w(x,u,∇gu)=0 in a Lorentzian manifold (M,g) with boundary, where ∇gu denotes gradient and w(x,u,ξ) is smooth quadratic ξ. Under appropriate assumptions, we show that conformal class of metric g can be recovered up to diffeomorphisms, from knowledge Neumann-to-Dirichlet map. With some additional conditions, recover itself diffeomorphi...

Sufficient and necessary conditions are provided on warped product manifolds their base fiber for a vector field $$\varphi _{j}$$ to be \left( \mathrm {Ric}\right) $$ -vector , that is, $$\nabla _{i}\varphi _{j}=\mu R_{ij}$$ where $$R_{ij}$$ is the Ricci tensor of M \mu scalar. Two space-times admitting fields considered. Lorentzian quasi-Einstein time-like {Ric} \right) shown either simple or ...

We explore singularity-free and geodesically-complete cosmologies based on manifolds that are not quite Lorentzian. The metric can be either smooth everywhere or non-degenerate everywhere, but both, depending the coordinate system. gives an Einstein tensor is first order in derivatives while has a piecewise FLRW form. On such manifold universe transition from expanding to contracting, vice vers...