Distribution (differential geometry)

About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.

TEC Forecasting Based on Manifold Trajectories

Abstract: In this paper, we present a method for forecasting the ionospheric Total Electron Content (TEC) distribution from the International GNSS Service’s Global Ionospheric Maps. The forecasting system gives an estimation of the value of the TEC distribution based on linear combination of previous TEC maps (i.e., a set of 2D arrays indexed by time), and the computation of a tangent subspace in a manifold associated to each map. The use of the tangent space to each map is justified because it allows modeling the possible distortions from one observation to the next as a trajectory on the tangent manifold of the map. The coefficients of the linear combination of the last observations along with the tangent space are estimated at each time stamp to minimize the mean square forecasting error with a regularization term. The estimation is made at each time stamp to adapt the forecast to short-term variations in solar activity.

Screen conformal lightlike submanifolds of semi-Riemannian manifolds

Abstract: Since the induced objects on a lightlike submanifold depend on its screen distribution which, in general, is not unique and hence we can not use the classical submanifold theory on a lightlike submanifold in the usual way. Therefore, in present paper, we study screen conformal lightlike submanifolds of a semi-Riemannian manifold, which are essential for the existence of unique screen distribution. We obtain a characterization theorem for the existence of screen conformal lightlike submanifolds of a semi-Riemannian manifold. We prove that if the differential operator Ds is a metric Otsuki connection on transversal lightlike bundle for a screen conformal lightlike submanifold then semi-Riemannian manifold is a semi-Euclidean space. We also obtain some characterization theorems for a screen conformal totally umbilical lightlike submanifold of a semi-Riemannian space form. Further, we obtain a necessary and sufficient condition for a screen conformal lightlike submanifold of constant curvature to be a semi-Euclidean space. Finally, we prove that for an irrotational screen conformal lightlike submanifold of a semi-Riemannian space form, the induced Ricci tensor is symmetric and the null sectional curvature vanishes.

Some framed f -structures on transversally Finsler foliations

Abstract: Some problems concerning to Liouville distribution and framed \(f\)-structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed \(f(3,\varepsilon)\)- structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.

Extension of distributions, scalings and renormalization of QFT on Riemannian manifolds

Abstract: Let $M$ be a smooth manifold and $X\subset M$ a closed subset of $M$. In this paper, we introduce a natural condition of \emph{moderate growth} along $X$ for a distribution $t$ in $\mathcal{D}^\prime(M\setminus X)$ and prove that this condition is equivalent to the existence of an extension of $t$ in $\mathcal{D}^\prime(M)$ generalizing some previous results of Meyer and Brunetti--Fredenhagen. When $X$ is a closed submanifold of $M$, we show that the concept of distributions with moderate growth coincides with weakly homogeneous distributions of Meyer. Then we renormalize products of distributions with functions tempered along $X$ and finally, using the whole analytical machinery developed, we give an existence proof of perturbative quantum field theories on Riemannian manifolds.