A certain complete space-like hypersurface in Lorentz manifolds.
A characterization of the Riemann extension in terms of harmonicity
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...
A class of metrics on tangent bundles of pseudo-Riemannian manifolds
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...
A classfication of 3-type curves in Minkowski 3-space . II.
A classification of 2-type curves in the Minkowski space .
A Classification of 2-type Curves in the Minkowski Space E1n
A classification of 3-type curves in Minkowski 3-space . I.
A classification of 3-type curves in Minkowski 3-space e_1^3, II
A complete classification of four-dimensional paraKähler Lie algebras
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.
A construction of transverse submanifolds.
A dynamical approach to compactify the three dimensional Lorentz group.
A gauge theoretical approach to space-time structures
A geodesic completeness theorem for locally symmetric Lorentz manifolds.
We prove that a locally symmetric and a null-complete Lorentz manifold is geodetically complete.
A hyperbolic twistor space.
A Morse theory for light rays on stably causal lorentzian manifolds
A new characterization of -stable hypersurfaces in space forms
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.
A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form
We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3].
A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary).
A recurrent curvature-like tensor on semi-definite Kähler manifolds.
A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold
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).