Cartan Geometries and their Symmetries: A Lie Algebroid by Mike Crampin,David Saunders

By Mike Crampin,David Saunders

In this publication we first overview the information of Lie groupoid and Lie algebroid, and the linked suggestions of connection. We subsequent give some thought to Lie groupoids of fibre morphisms of a  fibre package deal, and the connections on such groupoids including their symmetries. We additionally see how the infinitesimal procedure, utilizing Lie algebroids instead of Lie groupoids, and particularly utilizing Lie algebroids of vector fields alongside the projection of the fibre package, might be of benefit.
We then introduce Cartan geometries, including a few instruments we will use to check them. We take, as specific examples, the 4 classical forms of geometry: affine, projective, Riemannian and conformal geometry. We additionally see how our process can begin to healthy right into a extra basic concept. ultimately, we specialize to the geometries (affine and projective) linked to direction areas and geodesics, and think about their symmetries and different properties.

Read or Download Cartan Geometries and their Symmetries: A Lie Algebroid Approach (Atlantis Studies in Variational Geometry) PDF

Similar geometry & topology books

Manifolds all of whose Geodesics are Closed (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)

X 1 O S R Cher lecteur, J'entre bien tard dans l. a. sphere etroite des ecrivains au double alphabet, moi qui, il y a plus de quarante ans deja, avais accueilli sur mes terres un normal epris de mathematiques. JI m'avait parle de ses projets grandioses en promettant d'ailleurs de m'envoyer ses ouvrages de geometrie.

Mathematical Excursions to the World's Great Buildings

From the pyramids and the Parthenon to the Sydney Opera condo and the Bilbao Guggenheim, this publication takes readers on an eye-opening travel of the maths at the back of a number of the world's such a lot unbelievable constructions. superbly illustrated, the booklet explores the milestones in effortless arithmetic that brighten up the knowledge of those structures and combines this with an in-depth examine their aesthetics, heritage, and constitution.

The Mathematics of Knots: Theory and Application: 1 (Contributions in Mathematical and Computational Sciences)

The current quantity grew out of the Heidelberg Knot thought Semester, geared up via the editors in iciness 2008/09 at Heidelberg collage. The contributed papers carry the reader modern at the at the moment such a lot actively pursued parts of mathematical knot conception and its purposes in mathematical physics and phone biology.

Lectures on Algebraic Cycles (New Mathematical Monographs)

Spencer Bloch's 1979 Duke lectures, a milestone in sleek arithmetic, were out of print nearly in view that their first e-book in 1980, but they've got remained influential and are nonetheless the simplest position to profit the guiding philosophy of algebraic cycles and factors. This variation, now professionally typeset, has a brand new preface through the writer giving his viewpoint on advancements within the box over the last 30 years.

Additional resources for Cartan Geometries and their Symmetries: A Lie Algebroid Approach (Atlantis Studies in Variational Geometry)

Sample text