On some applications of Bochner-Schoenberg-Eberlein type theorems
On some form determined by a distribution on a Riemannian manifold
On some property of the tangency relation of sets.
On space forms of Grassmann manifolds.
On special Riemannian -manifolds with distinct constant Ricci eigenvalues
The first author and F. Prufer gave an explicit classification of all Riemannian 3-manifolds with distinct constant Ricci eigenvalues and satisfying additional geometrical conditions. The aim of the present paper is to get the same classification under weaker geometrical conditions.
On subharmonic functions and differential geometry in the large.
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 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 characteristic function of spaces of constant holomorphic curvature
On the characterizations of flat metrics by the spectrum.
On the Construction of Harmonie and Holomorphic Maps Between Surfaces.
On the continuity of harmonic mappings and the Boundary.
On the curvature of the space of qubits
The Fisher informational metric is unique in some sense (it is the only Markovian monotone distance) in the classical case. A family of Riemannian metrics is called monotone if its members are decreasing under stochastic mappings. These are the metrics to play the role of Fisher metric in the quantum case. Monotone metrics can be labeled by special operator monotone functions, according to Petz's Classification Theorem. The aim of this paper is to present an idea how one can narrow the set of monotone...
On the Differentiable Pinching Problem.
On the differential geometry of frame bundles of Riemannian manifolds.
On the Dirichlet Problem at Infinity for Manifolds of Nonpositive Curvature.
On the Elliptic Equation ...u + K(x)e2u = 0 and Conformal Metrics with Prescribed Gaussian Curvatures..
On the energy of sections of trivializable sphere bundles.
On the energy of unit vector fields with isolated singularities
We consider the energy of a unit vector field defined on a compact Riemannian manifold M except at finitely many points. We obtain an estimate of the energy from below which appears to be sharp when M is a sphere of dimension >3. In this case, the minimum of energy is attained if and only if the vector field is totally geodesic with two singularities situated at two antipodal points (at the 'south and north pole').
On the Ergodicity of Frame Flows.