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The automorphism groups of foliations with transverse linear connection

Nina Zhukova, Anna Dolgonosova (2013)

Open Mathematics

The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian foliations.

The resolution of the bounded L 2 curvature conjecture in general relativity

Sergiu Klainerman, Igor Rodnianski, Jérémie Szeftel (2014/2015)

Séminaire Laurent Schwartz — EDP et applications

This paper reports on the recent proof of the bounded L 2 curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the L 2 -norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.

The spacetime positive mass theorem in dimensions less than eight

Michael Eichmair, Lan-Hsuan Huang, Dan A. Lee, Richard Schoen (2016)

Journal of the European Mathematical Society

We prove the spacetime positive mass theorem in dimensions less than eight. This theorem asserts that for any asymptotically flat initial data set that satisfies the dominant energy condition, the inequality E ≥ P holds, where ( E , P ) is the ADM energy-momentum vector. Previously, this theorem was only known for spin manifolds [38]. Our approach is a modification of the minimal hypersurface technique that was used by the last named author and S.-T. Yau to establish the time-symmetric case of this theorem...

Timelike B 2 -slant helices in Minkowski space E 1 4

Ahmad T. Ali, Rafael López (2010)

Archivum Mathematicum

We consider a unit speed timelike curve α in Minkowski 4-space 𝐄 1 4 and denote the Frenet frame of α by { 𝐓 , 𝐍 , 𝐁 1 , 𝐁 2 } . We say that α is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction U of 𝐄 1 4 . In this work we study those helices where the function 〈 𝐁 2 , U 〉 is constant and we give different characterizations of such curves.

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