An alternative moving frame for tubular surfaces around time-like curves in the Minkowski 3-space.
An example of an almost hyperbolic Hermitian manifold.
An explicit classification of 3-dimensional Riemannian spaces satisfying
An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy Huygens' principle. Part I : Petrov type N background space-times
An explicit determination of the Petrov type D spacetimes on which Weyl's neutrino equation and Maxwell's equations satisfy Huygens' principle
An extension of a theorem concerning conformal pseudo-Riemannian metrics. (Une extension d'un théorème concernant les métriques pseudoriemanniennes conformes.)
An Osserman-type condition on g.f.f-manifolds with Lorentz metric
A condition of Osserman type, called the φ-null Osserman condition, is introduced and studied in the context of Lorentz globally framed f-manifolds. An explicit example shows the naturality of this condition in the setting of Lorentz 𝓢-manifolds. We prove that a Lorentz 𝓢-manifold with constant φ-sectional curvature is φ-null Osserman, extending a well-known result in the case of Lorentz Sasaki space forms. Then we state a characterization of a particular class of φ-null Osserman 𝓢-manifolds....
Angles and quasiconformal mappings on Riemannian manifolds
Another Look at Connections
Anti-invariant Riemannian submersions from almost Hermitian manifolds
We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold...
Application of spaces of subspheres to conformal invariants of curves and canal surfaces
We review some techniques from the Möbius geometry of curves and surfaces in the 3-sphere, consider canal surfaces using their characteristic circles, and express the conformal curvature, and conformal torsion, of a vertex-free space curve in terms of its corresponding curve of osculating circles, and osculating spheres, respectively. We accomplish all of this strictly within the framework of Möbius geometry, and compare our results with the literature. Finally, we show how our formulation allows...
Application of the Weyl curvature tensor to description of the generalized Reissner-Nordstrøm space-time
The Weyl curvature tensor for the generalized Reissner-Nordstrοm space-time is determined and theorems related to the Penrose conjecture are proved.
Applications of spectral geometry to affine and projective geometry.
Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds
To any smooth compact manifold endowed with a contact structure and partially integrable almost CR structure , we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric on . We consider the asymptotic expansion, in powers of a special defining function, of the volume of with respect to and prove that the log term coefficient is independent of (and any choice of contact...
Area-stationary surfaces in neutral Kähler 4-manifolds.
Autour de la conjecture de L. Markus sur les variétés affines.