Curvature: A Variational Approach

By Andrei A. Agrachev, Davide Barilari, L. Rizzi. Memoirs of the American Mathematical Society, 2013

103 citations recorded by the source corpus.

The curvature discussed in this paper is a rather far going generalization of the Riemann 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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Genetics

View Paper: https://www.semanticscholar.org/paper/f9f7dc5e11eef8e132bb04b1f3d176ef4829b54f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Davide Barilari
2. Ugo V. Boscain
3. L. Rizzi
4. Andrei A. Agrachev
5. Robert W. Neel
6. Igor Zelenko
7. Fabrice Baudoin
8. Enrico Le Donne

In Astronomy and Astrophysics

1. Davide Barilari
2. L. Rizzi
3. Ugo V. Boscain
4. Andrei A. Agrachev
5. Igor Zelenko
6. R. B. Tully
7. Gregoire Charlot
8. Roberta Ghezzi

In Genetics

1. Davide Barilari
2. L. Rizzi
3. Andrei A. Agrachev

Citations in the corpus

• A Comprehensive Introduction to Sub-Riemannian Geometry (2019, background): “The reader is referred also to [ABR18] and [ABR17] for a discussion of the higher dimensional contact case.”
• Sub-Riemannian interpolation inequalities (2017, methodology): “The geodesic dimension is an invariant initially discovered for sub-Riemannian structures in [ABR13], and subsequentely generalized to metric measure spaces in [Riz16].”