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Geometry on Manifolds
Hansjörg Geiges (Gebundene Ausgabe, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
27.08.2026
Sprache
Englisch
EAN
9783032242341
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Compact Textbooks in Mathematics
Sonderedition
Nein
Autor
Hansjörg Geiges
Seitenanzahl
235
Einbandart
Broschiert
Buch Untertitel
Riemannian Metrics, Symplectic Forms, Contact Structures
Schlagwörter
Differential manifolds, Vector bundles, Tensors, Riemannian manifolds, Symplectic linear algebra, Geodesics
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer Nature Switzerland AG, Europaplatz 3,69115 Heidelberg, Germany, Heidelberg, Deutschland, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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