A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings

This article is devoted to geometrical aspects of conformal mappings of complete Riemannian and Kählerian manifolds and uses the Bochner technique, one of the oldest and most important techniques in modern differential geometry. A feature of this article is that the results presented here are easily obtained using a generalized version of the Bochner technique due to theorems on the connection between the geometry of a complete Riemannian manifold and the global behavior of its subharmonic, superharmonic, and convex functions.

Application of the Generalized Bochner Technique to the Study of Conformally Flat Riemannian Manifolds

In this article, we discuss the global aspects of the geometry of locally conformally flat (complete and compact) Riemannian manifolds. In particular, the article reviews and improves some results (e.g., the conditions of compactness and degeneration into spherical or flat space forms) on the geometry “in the large" of locally conformally flat Riemannian manifolds. The results presented here were obtained using the generalized and classical Bochner technique, as well as the Ricci flow.

Riemannian foliations and the kernel of the basic Dirac operator

In this paper, in the special setting of a Riemannian foliation en- dowed with a bundle-like metric, we obtain conditions that force the vanishing of the kernel of the basic Dirac operator associated to the metric; this way we extend the traditional setting of Riemannian foli- ations with basic-harmonic mean curvature, where Bochner technique and vanishing results are known to work. Beside classical conditions concerning the positivity of some curvature terms we obtain new rela- tions between the mean curvature form and the kernel of the basic Dirac operator

HARMONIC ANALYSIS OF THE LEBEDEV-STIELTJES INTEGRALS

We expand the Bochner technique on the following Lebedev-Stieltjes integrals [Formula: see text] which are related to the Kontorovich-Lebedev transformation. Mapping and inversion properties are investigated. The Fourier type series with respect to an uncountable orthonormal system of the modified Bessel functions are considered in the Bohr type pre-Hilbert space. The Bessel inequality and Parseval equality are proved.