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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 holds, where 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...
We consider a unit speed timelike curve in Minkowski 4-space and denote the Frenet frame of by . We say that is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction of . In this work we study those helices where the function is constant and we give different characterizations of such curves.
We study totally contact umbilical screen-slant lightlike submanifolds and totally contact umbilical screen-transversal lightlike submanifolds of an indefinite Kenmotsu manifold. We prove a characterization theorem of totally contact umbilical screen-slant lightlike submanifolds of an indefinite Kenmotsu manifold. We further prove some results on a totally contact umbilical radical screen-transversal lightlike submanifold of an indefinite Kenmotsu manifold, such as the necessary and sufficient conditions...
For (M, [g]) a conformal manifold of signature (p, q) and dimension at least three, the conformal holonomy group Hol(M, [g]) ⊂ O(p + 1, q + 1) is an invariant induced by the canonical Cartan geometry of (M, [g]). We give a description of all possible connected conformal holonomy groups which act transitively on the Möbius sphere S p,q, the homogeneous model space for conformal structures of signature (p, q). The main part of this description is a list of all such groups which also act irreducibly...
Le but de cet article est d’exposer de nouveaux exemples de structures anti-de Sitter sur des fibrés en cercles au-dessus d’une surface hyperbolique qui ne sont pas, modulo revêtement et quotient finis, des déformations de structures homogènes.
Connected weakly irreducible not irreducible subgroups of that satisfy a certain additional condition are classified. This will be used to classify connected holonomy groups of pseudo-hyper-Kählerian manifolds of index 4.
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