k-Symplectic Affine Manifolds

Azzouz Awane and Michel Goze
Additional contact information
Azzouz Awane: Université Hassan II, Faculté des Sciences
Michel Goze: Université de Haute Alsace, Faculté des Sciences et Techniques

Chapter Chapter 7 in Pfaffian Systems, k-Symplectic Systems, 2000, pp 173-190 from Springer

Abstract: Abstract Let M be a smooth manifold of dimension n. We say that M is an affine manifold if there is an atlas (U i, φ i) of M such that the changes of coordinates are restrictions of affine transformations of ∝ n . An affine structure on M is equivalent to a given connection $$\nabla \Gamma (TM) \times \Gamma (TM) \to \Gamma (TM)$$ such that both the curvature $$k(X,Y) = {\nabla _{\left[ {X,Y} \right]}} - ({\nabla _X}{\nabla _Y} - {\nabla _Y}{\nabla _X})$$ and torsion $$T(X,Y) = {\nabla _X}Y - {\nabla _Y}X - [X,Y]$$ vanish identically.

Keywords: Fundamental Group; Affine Transformation; Characteristic Foliation; Flat Connection; Affine Structure (search for similar items in EconPapers)
Date: 2000
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9526-1_7

Ordering information: This item can be ordered from
http://www.springer.com/9789401595261

DOI: 10.1007/978-94-015-9526-1_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().