Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 6 - The Künneth Connection

  • M. J. D. Hamilton, Universität Stuttgart, D. Kotschick, Ludwig-Maximilians-Universität München
  • Book:
    Künneth Geometry
    Published online:
    07 December 2023
    Print publication:
    21 December 2023, pp 73-84

  • Summary

    In this chapter we discuss the unique torsion-free affine connection defined by a Künneth structure. This connection, which we call the Künneth connection, preserves the two foliations and is compatible with the symplectic structure. We will actually start with a more general setup, proving that for every almost Künneth structure there is a distinguished connection for which the whole structure is parallel. It then turns out that this connection is torsion-free if and only if the almost Künneth structure is integrable, i.e. it arises tautologically from a Künneth structure. In this case the Künneth connection is just the Levi-Civita connection of the associated pseudo-Riemannian metric.

    In the final section of this chapter we use connections to prove that Künneth or bi-Lagrangian structures are in fact the same as para-Kähler structures.