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# ðŸ“™ Sub-Riemannian Geometry by Andre Bellaiche, Jean-Jaques Risler â€” free epub

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Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely:
â€¢ control theory â€¢ classical mechanics â€¢ Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) â€¢ diffusion on manifolds â€¢ analysis of hypoelliptic operators â€¢ Cauchy-Riemann (or CR) geometry.
Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics.
This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists:
â€¢ AndrÃ© BellaÃ¯che: The tangent space in sub-Riemannian geometry â€¢ Mikhael Gromov: Carnot-CarathÃ©odory spaces seen from within â€¢ Richard Montgomery: Survey of singular geodesics â€¢ HÃ©ctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers â€¢ Jean-Michel Coron: Stabilization of controllable systems

## About book:

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- Series:
**Progress in Mathematics** - Author:
**Andre Bellaiche, Jean-Jaques Risler** - Year:
**1996** - Publisher:
**BirkhÃ¤user Basel** - Language:
**English** - ISBN:
**9783764354763,3764354763**

- File size:
**278 809** - Format:
**pdf**

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Non-Riemannian Geometry deals basically with manifolds dominated by the geometry of paths co-developed by the distinguished mathematician Luther Pfahler Eisenhart, the author of this text. He begins with a consideration of asymmetric connections, and then...

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability ...

For a Riemannian manifold $M$, the geometry, topology and analysis are interrelated in ways that are widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the ...

"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspecti...

The study of curves and surfaces forms an important part of classical differential geometry. Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in this field along with important ideas of Riemannian geometry. The r...

This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of t...

"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspecti...

A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including ske...

A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including ske...

Anger, Rage and Relationship presents a radically new way to understand and work with anger and rage issues. Taking a relational approach to anger and rage, the book presents a positive view of human nature, supported by recent research findings and illus...

A New York Times Notable Book of the Year"Resolution can stand alone, battered and proud, as a class-conscious crime novel that dares to tell the ugly truth." -New York Times Book ReviewJust as Maureen O'Donnell is struggling to give up drinking, she face...

In a study of Africa's political and religious past, Christopher Wrigley uses local traditions and comparative mythology to explore an ancient system of myth and ritual in the precolonial kingdom of Buganda, the nucleus of modern Uganda. The study include...

B-movies, crime novels, science fiction- all of these forms of mass media came into their own in the 1950s. Dismissed by critics as dehumanizing to both author and audience, these genres unflinchingly exposed the depths of American life at a time when ...

"Bennett interviewed women in Manchester, England, asking them about ghosts and other supernatural experiences and beliefs. (Her discussion of how her research methods and interview techniques evolved is in itself valuable.) She first published the result...

This study offers a comprehensive reconsideration of the life and literary works of Paulinus of Nola (ca. 352-431), a Roman senator who renounced his political career and secular lifestyle to become a monk, bishop, impresario of a saint's cult, and promin...

Thompson examines the U.S. role--both governmental and that of Irish-Americans--in attempting to bring a resolution to the strife in Northern Ireland. He concentrates on the efforts since 1967, particularly the growth of American efforts to become the cen...

"an excellent work . . . mercifully free of abstract pontification. . . . [The University of California] Vietnam War Archive, with its sections on psychological warfare; propaganda analysis; political warfare; the VC's political dau tranh or struggle stra...