Davide Barilari's Books

A Comprehensive Introduction to Sub-Riemannian Geometry

By: Andrei Agrachev,Davide Barilari,Ugo Boscain

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A Comprehensive Introduction to Sub-Riemannian Geometry

By: Andrei Agrachev,Davide Barilari,Ugo Boscain

Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several areas of pure and applied mathematics, with applications to many areas such as quantum control, Hamiltonian dynamics, robotics and Lie theory. This comprehensive introduction proceeds from classical topics to cutting-edge theory and applications, assuming only standard knowledge of calculus, linear algebra and differential equations. The book may serve as a basis for an introductory course in Riemannian geometry or an advanced course in sub-Riemannian geometry, covering elements of Hamiltonian dynamics, integrable systems and Lie theory. It will also be a valuable reference source for researchers in various disciplines.

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765

Publisher

Cambridge University Press

Published Date

ISBN 10

1108757251

ISBN 13

9781108757256

A Comprehensive Introduction to Sub-Riemannian Geometry

By: Andrei Agrachev,Davide Barilari,Ugo Boscain

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A Comprehensive Introduction to Sub-Riemannian Geometry

By: Andrei Agrachev,Davide Barilari,Ugo Boscain

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Page Count

765

Publisher

Cambridge University Press

Published Date

ISBN 10

1108757251

ISBN 13

9781108757256

Curvature: A Variational Approach

By: A. Agrachev,D. Barilari,L. Rizzi

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Curvature: A Variational Approach

By: A. Agrachev,D. Barilari,L. Rizzi

The curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces. Special attention is paid to the sub-Riemannian (or Carnot–Carathéodory) metric spaces. The authors' construction of curvature is direct and naive, and similar to the original approach of Riemann. In particular, they extract geometric invariants from the asymptotics of the cost of optimal control problems. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.

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Page Count

154

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470426463

ISBN 13

9781470426460

Book's by Davide Barilari

A Comprehensive Introduction to Sub-Riemannian Geometry

A Comprehensive Introduction to Sub-Riemannian Geometry

A Comprehensive Introduction to Sub-Riemannian Geometry

A Comprehensive Introduction to Sub-Riemannian Geometry

Curvature: A Variational Approach

Curvature: A Variational Approach

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