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

  • A Decomposition Theorem for Immersions of Product Manifolds

  • Part of
  • Ruy Tojeiro
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 1 / February 2016
    Published online by Cambridge University Press:
    17 April 2015, pp. 247-269

  • We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally or globally decomposed as a product manifold endowed with a polar metric. For such a product manifold, our main result gives a complete description of all its isometric immersions into a space form whose second fundamental forms are adapted to its product structure in the sense that the tangent spaces to each factor are preserved by all shape operators. This is a far-reaching generalization of a basic decomposition theorem for isometric immersions of Riemannian products due to Moore as well as of its extension by Nölker to isometric immersions of warped products.