A certain complete space-like hypersurface in Lorentz manifolds.
If is a manifold with a symmetric linear connection, then can be endowed with the natural Riemann extension (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to initiated by C. L. Bejan and O. Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure on and prove that is harmonic (in the sense of E. García-Río, L. Vanhecke and M. E. Vázquez-Abal (1997)) if and only if reduces to the...
We provide the tangent bundle of pseudo-Riemannian manifold with the Sasaki metric and the neutral metric . First we show that the holonomy group of contains the one of . What allows us to show that if is indecomposable reducible, then the basis manifold is also indecomposable-reducible. We determine completely the holonomy group of according to the one of . Secondly we found conditions on the base manifold under which ( respectively ) is Kählerian, locally symmetric or Einstein...
We consider paraKähler Lie algebras, that is, even-dimensional Lie algebras g equipped with a pair (J, g), where J is a paracomplex structure and g a pseudo-Riemannian metric, such that the fundamental 2-form Ω(X, Y) = g(X, JY) is symplectic. A complete classification is obtained in dimension four.
We prove that a locally symmetric and a null-complete Lorentz manifold is geodetically complete.
In this paper we study the -stability of closed hypersurfaces with constant -th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the -stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the -th mean curvature.
We consider a certain pseudo-Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g) and obtain necessary and sufficient conditions for the pseudo-Riemannian manifold (TM,G) to be Ricci flat (see Theorem 2).
A new class of relativistic diffusions encompassing all the previously studied examples has recently been introduced in the article of C. Chevalier and F. Debbasch (J. Math. Phys. 49 (2008) 043303), both in a heuristic and analytic way. A stochastic approach of these processes is proposed here, in the general framework of lorentzian geometry. In considering the dynamics of the random motion in strongly causal spacetimes, we are able to give a simple definition of the one-particle distribution function...