On the Arnold conjecture for weakly monotone symplectic manifolds.
On the asymptotic behavior of Dirichlet problems in a riemannian manifold less small random holes
On the asymptotic geometry of gravitational instantons
We investigate the geometry at infinity of the so-called “gravitational instantons”, i.e. asymptotically flat hyperkähler four-manifolds, in relation with their volume growth. In particular, we prove that gravitational instantons with cubic volume growth are ALF, namely asymptotic to a circle fibration over a Euclidean three-space, with fibers of asymptotically constant length.
On the Atiyah-Hitchin-Drinfeld-Manin Vanishing Theorem for Cohomology Groups of Instanton Bundles.
On the automorphism group of a compact Lorentz manifold and other geometric.
On the automorphism group of a second order structure
On the automorphism group of strongly pseudoconvex domains in almost complex manifolds
In contrast with the integrable case there exist infinitely many non-integrable homogeneous almost complex manifolds which are strongly pseudoconvex at each boundary point. All such manifolds are equivalent to the Siegel half space endowed with some linear almost complex structure.We prove that there is no relatively compact strongly pseudoconvex representation of these manifolds. Finally we study the upper semi-continuity of the automorphism group of some hyperbolic strongly pseudoconvex almost...
On the biharmonicity of product maps.
On the bochner conformal curvature of Kähler-Norden manifolds
Using the one-to-one correspondence between Kähler-Norden and holomorphic Riemannian metrics, important relations between various Riemannian invariants of manifolds endowed with such metrics were established in my previous paper [19]. In the presented paper, we prove that there is a strict relation between the holomorphic Weyl and Bochner conformal curvature tensors and similarly their covariant derivatives are strictly related. Especially, we find necessary and sufficient conditions for the holomorphic...
On the Busemann area in Minkowski spaces.
On the Cartan-Norden theorem for affine Kähler immersions
In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.
On the casual structure of homogeneous manifolds.
On the causal structure of Lorentzian Lie groups. A globality theorem for Lorentzian cones in certain solvable Lie algebras.
On the central paths and Cauchy trajectories in semidefinite programming
In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a particular case of convex programming with conic constraints. The studied class of functions consists of spectrally defined functions induced by penalty or barrier...
On the characteristic connection of gwistor space
We give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T c is ∇c-parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.
On the characteristic function of spaces of constant holomorphic curvature
On the characterizations of flat metrics by the spectrum.
On the Chen character of –ideal submanifolds
On the Chern Forms of Kaehler Hypersurfaces in Complex Space Forms.
On the Chern-type problem in a complex projective space.