8 citations · 30 across the 18 of their papers we have counts for
20 papers
Fedosov manifolds with parallel symplectic Weyl curvature
Shane Rankin, Ivo Terek
A classical 1977 result by Roter states that a Riemannian manifold of dimension at least four with parallel Weyl curvature must be locally symmetric or conformally flat. We establi…
The curvature of left-invariant magnetic systems
Shane Rankin, Ivo Terek, David Weed
We compute the magnetic curvatures (in the sense of Assenza) of left-invariant magnetic systems on Lie groups and explore relations between curvature properties and algebraic prope…
Finiteness of Totally Magnetic Hypersurfaces
James Marshall Reber, Ivo Terek
By introducing a dynamical version of the second fundamental form, we generalize a recent result of Filip-Fisher-Lowe to the setting of magnetic systems. Namely, we show that a rea…
The submanifold compatibility equations in magnetic geometry
Ivo Terek
With the notions of magnetic curvature and magnetic second fundamental form recently introduced by Assenza and Albers-Benedetti-Maier, respectively, we establish analogues of the G…
Parallel differential forms of codegree two, and three-forms in dimension six
Andrzej Derdzinski, Paolo Piccione, Ivo Terek
For a differential form on a manifold, having constant components in suitable local coordinates trivially implies being parallel relative to a torsion-free connection, and the conv…
Marked length spectrum rigidity for Anosov magnetic surfaces
Valerio Assenza, Jacopo de Simoi, James Marshall Reber +1
We show that if is a closed, connected, oriented surface, and two Anosov magnetic systems on are conjugate by a volume-preserving conjugacy isotopic to the identity, with t…
Nijenhuis geometry of parallel tensors
Andrzej Derdzinski, Paolo Piccione, Ivo Terek
A tensor -- meaning here a tensor field of any type on a manifold -- may be called integrable if it is parallel relative to some torsion-free connection. We provide ana…
Compact plane waves with parallel Weyl curvature
Ivo Terek
This is an exposition of recent results -- obtained in joint work with Andrzej Derdzinski -- on essentially conformally symmetric (ECS) manifolds, that is, those pseudo-Riemannian…
Corrections of minor misstatements in several papers on ECS manifolds
Andrzej Derdzinski, Ivo Terek
In the paper [3] the value of the invariant denoted by d and often called "rank" was misstated for a narrow class of examples of ECS manifolds: they were identified as having d = 1…
Magnetic flatness and E. Hopf's theorem for magnetic systems
Valerio Assenza, James Marshall Reber, Ivo Terek
Using the notion of magnetic curvature recently introduced by the first author, we extend E. Hopf's theorem to the setting of magnetic systems. Namely, we prove that if the magneti…
Killing fields on compact pseudo-Kähler manifolds
Andrzej Derdzinski, Ivo Terek
We show that a Killing field on a compact pseudo-Kähler ddbar manifold is necessarily (real) holomorphic. Our argument works without the ddbar assumption in real dimension four. Th…
Codazzi tensor fields in reductive homogeneous spaces
James Marshall Reber, Ivo Terek
We extend the results about left-invariant Codazzi tensor fields on Lie groups equipped with left-invariant Riemannian metrics obtained by d'Atri in 1985 to the setting of reductiv…
Compact locally homogeneous manifolds with parallel Weyl tensor
Andrzej Derdzinski, Ivo Terek
We construct new examples of compact ECS manifolds, that is, of pseudo-Riemannian manifolds with parallel Weyl tensor that are neither conformally flat nor locally symmetric. Every…
The metric structure of compact rank-one ECS manifolds
Andrzej Derdzinski, Ivo Terek
Pseudo-Riemannian manifolds with nonzero parallel Weyl tensor which are not locally symmetric are known as ECS manifolds. Every ECS manifold carries a distinguished null parallel d…
Rank-one ECS manifolds of dilational type
Andrzej Derdzinski, Ivo Terek
We study ECS manifolds, that is, pseudo-Riemannian manifolds with parallel Weyl tensor which are neither conformally flat nor locally symmetric. Every ECS manifold has rank 1 or 2,…
Conformal flatness of compact three-dimensional Cotton-parallel manifolds
Ivo Terek
A three-dimensional pseudo-Riemannian manifold is called essentially conformally symmetric (ECS) if its Cotton tensor is parallel but nowhere-vanishing. In this note we prove that…
The topology of compact rank-one ECS manifolds
Andrzej Derdzinski, Ivo Terek
Pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric, also known as ECS manifolds, have a natural local invariant, the rank, whi…
New examples of compact Weyl-parallel manifolds
Andrzej Derdzinski, Ivo Terek
We prove the existence of compact pseudo-Riemannian manifolds with parallel Weyl tensor which are neither conformally flat nor locally symmetric, and represent all indefinite metri…
Topics in Lorentz Geometry
Ivo Terek
Lecture notes from the mini-course "Topics in Lorentz Geometry" taught at the University of São Paulo, in March/2019. The text has three parts: (i) an overall view of linear algebr…
A local characterization for constant curvature metrics in 2-dimensional Lorentz manifolds
Ivo Terek, Alexandre Lymberopoulos
In this paper we define Fermi-type coordinates in a 2-dimensional Lorentz manifold, and use this coordinate system to provide a local characterization of constant Gaussian curvatur…