@article {BARILARI2017118,
	title = {Curvature terms in small time heat kernel expansion for a model class of hypoelliptic H{\"o}rmander operators},
	journal = {Nonlinear Analysis},
	volume = {164},
	year = {2017},
	pages = {118 - 134},
	abstract = {<p>We consider the heat equation associated with a class of second order hypoelliptic H{\"o}rmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.</p>},
	keywords = {Curvature, Hypoelliptic heat equation, Small time asymptotics},
	issn = {0362-546X},
	doi = {https://doi.org/10.1016/j.na.2017.09.002},
	url = {http://www.sciencedirect.com/science/article/pii/S0362546X17302298},
	author = {Davide Barilari and Elisa Paoli}
}
@article {2013,
	title = {The curvature: a variational approach},
	number = {arXiv:1306.5318;},
	year = {2013},
	note = {88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections
  on Finsler manifolds, slow growth distributions, Heisenberg group},
	institution = {SISSA},
	abstract = {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 such as
Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special
attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces.
Our construction of the curvature is direct and naive, and it is similar to the
original approach of Riemann. Surprisingly, it works in a very general setting
and, in particular, for all sub-Riemannian spaces.},
	keywords = {Crurvature, subriemannian metric, optimal control problem},
	url = {http://hdl.handle.net/1963/7226},
	author = {Andrei A. Agrachev and Davide Barilari and Luca Rizzi}
}
