Browsing by Author "Agrachev, Andrei A."

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The curvature: a variational approach

Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca (SISSA, 2013-06-22)

The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures ...
Geodesics and admissible-path spaces in Carnot Groups

Agrachev, Andrei A.; Gentile, A.; Lerario, Antonio (SISSA, 2013-11-26)

We study the topology of admissible-loop spaces on a step-two Carnot group G. We use a Morse-Bott theory argument to study the structure and the number of geodesics on G connecting the origin with a 'vertical' point ...
Introduction to Riemannian and sub-Riemannian geometry

Agrachev, Andrei A.; Barilari, Davide; Boscain, Ugo (SISSA, 2012-04)
Quadratic cohomology

Agrachev, Andrei A. (SISSA, 2013-01-10)

We study homological invariants of smooth families of real quadratic forms as a step towards a "Lagrange multipliers rule in the large" that intends to describe topology of smooth vector functions in terms of scalar ...

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