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
×
Home
  • Home
Hostname: page-component-77ffc5d9c7-5dsxc Total loading time: 0.73 Render date: 2021-04-23T16:43:30.157Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Bulletin of the Australian Mathematical Society Bulletin of the Australian Mathematical Society

Article contents

A Riemannian invariant and its applications to Einstein manifolds

Published online by Cambridge University Press:  17 April 2009

Bang-Yen Chen
Bang-Yen Chen
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824–1027, United States of America, e-mail: bychen@math.msu.edu
Corresponding
E-mail address:
bychen@math.msu.edu
Save pdf (0.4 megabytes)Save pdf (0.4 mb)
Rights & Permissions[Opens in a new window]

Extract

We introduce a Riemannian invariant and establish general optimal inequalities involving the invariants and the squared mean curvature for Einstein manifolds isometrically immersed in real space forms. We show that these inequalities do not hold for arbitrary submanifolds in real space forms in general. We also provide some immediate applications of the inequalities.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 55 - 65
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Chen, B.Y., Geometry of submanifolds (M. Dekker, New York, 1973).Google Scholar
[2]Chen, B.Y., ‘Some new obstructions to minimal and Lagrangian isometric immersions’, Japan. J. Math. 26 (2000), 105–127.CrossRefGoogle Scholar
[3]Chen, B.Y., ‘On isometric minimal immersions from warped products into real space forms’, Proc. Edinburgh Math. Soc. 45 (2002), 579–587.CrossRefGoogle Scholar
[4]Chen, B.Y., ‘Non-immersion theorems for warped products in complex hyperbolic spaces’, Proc. Japan Acad. Ser. A Math. Sci. 79 (2002), 96–100.CrossRefGoogle Scholar
[5]Chen, B.Y., ‘A general optimal inequality for warped products in complex projective spaces and its applications’, Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), 89–94.CrossRefGoogle Scholar
[6]Chen, B.Y., ‘A general inequality for conformally flat submanifolds and its applications’ (to appear).Google Scholar
[7]Gromov, M., ‘Isometric immersions of Riemannian manifolds, Elie Cartan et les Mathématiques d'Aujourd'hui’, Astérisque (1985), 129–133.Google Scholar
[8]Nagano, T., ‘On the minimum eigenvalues of the Laplacians in Riemannian manifolds’, Sci. Papers Coll. Gen. Edu. Univ. Tokyo 11 (1961), 177–182.Google Scholar
[9]Nash, J.F., ‘The imbedding problem for Riemannian manifolds’, Ann. of Math. 63 (1956), 20–63.CrossRefGoogle Scholar
[10]Yau, S.T., ‘Mathematical research today and tomorrow’, in Viewpoints of Seven Fields Medalists (Berlin, Heidelberg, New York, 1991), pp. 30–39.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 84 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 23rd April 2021. This data will be updated every 24 hours.

You have Access
2
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A Riemannian invariant and its applications to Einstein manifolds
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

A Riemannian invariant and its applications to Einstein manifolds
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

A Riemannian invariant and its applications to Einstein manifolds
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *