The curvature discussed in this paper is a far reaching generalisation of the Riemannian
sectional curvature. We give a unified definition of curvature which applies to a wide class of …

The author proved in the late 1980s that any homogeneous manifold with an intrinsic metric
is isometric to some homogeneous quotient space of a connected Lie group by its compact …

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We develop a variational theory of geodesics for the canonical variation of the metric of a
totally geodesic foliation. As a consequence, we obtain comparison theorems for the …

In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like
invariants. We show that these coefficients can be interpreted as the curvature of a canonical …

The monograph is devoted to the study of stochastic area functionals of Brownian motions
and of the associated heat kernels on Lie groups and Riemannian manifolds. It is essentially …

A classical aspect of Riemannian geometry is the study of estimates that hold uniformly over
some class of metrics. The best known examples are eigenvalue bounds under curvature …

With a view toward sub-Riemannian geometry, we introduce and study H-type foliations.
These structures are natural generalizations of K-contact geometries which encompass as …

Each sub-Riemannian geometry with bracket generating distribution enjoys a background
structure determined by the distribution itself. At the same time, those geometries with …

On H-type sub-Riemannian manifolds we establish sub-Hessian and sub-Laplacian
comparison theorems which are uniform for a family of approximating Riemannian metrics …