Geometry on Manifolds Riemannian Metrics, Symplectic Forms, Contact Structures
-
- Englisch ausgewählt
54,99 €
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
27.08.2026
Verlag
SpringerSeitenzahl
235
Maße (L/B)
23,5/15,5 cm
Sprache
Englisch
ISBN
978-3-032-24234-1
This first course on differential geometry includes not only Riemannian manifolds, but also symplectic and contact geometry. Rather than treating these three fields of geometry as separate subjects, this text emphasises common features by organising the material according to ideas and methods shared by the three fields.
Specifically, this text highlights how certain concepts, such as structure-preserving vector fields or variational characterisations of curves adapted to a given geometric structure, find their analogous expressions in the respective field of geometry. For example, Frobenius integrability, which is primarily relevant for contact geometry, is discussed together with the classification of flat Riemannian manifolds, which requires very similar arguments.
Another case in point is the discussion of transformation groups (isometries, symplectomorphisms, contactomorphisms) and the corresponding Lie algebras. Two equivalent ways to construct this Lie algebra structure are described: from the usual Lie bracket of vector fields on the manifold, restricted to the subalgebra of structure-preserving ones, or from the right-invariant vector fields on the transformation group.
This book also provides a concise introduction to manifolds, vector bundles, differential forms and tensors. As a result, it contains more material than can be covered in a single semester, and it is possible to teach various courses from it, depending on the background knowledge one may want to assume. Many examples and exercises are integrated into the richly illustrated text, making the book suitable for self-study.
Noch keine Bewertungen vorhanden
Verfassen Sie die erste Bewertung zu diesem Artikel
Helfen Sie anderen Kundinnen und Kunden durch Ihre Meinung.
Kurze Frage zu unserer Seite
Vielen Dank für Ihr Feedback
Wir nutzen Ihr Feedback, um unsere Produktseiten zu verbessern. Bitte haben Sie Verständnis, dass wir Ihnen keine Rückmeldung geben können. Falls Sie Kontakt mit uns aufnehmen möchten, können Sie sich aber gerne an unseren Kund*innenservice wenden.
zum Kundenservice