Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Critical mappings of Riemannian manifolds

Author: David D. Bleecker
Journal: Trans. Amer. Math. Soc. 254 (1979), 319-338
MSC: Primary 58E20; Secondary 53C20, 58D15
MathSciNet review: 539921
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider maps, from one Riemannian manifold to another, which are critical for all invariantly defined functionals on the space of maps. There are many such critical mappings, perhaps too numerous to suitably classify, although a characterization of sorts is provided. They are proven to have constant rank, with the image being a homogeneous minimal submanifold of the target manifold. Critical maps need not be Riemannian submersions onto their images. Also, there are homogeneous spaces for which the identity map is not critical. Many open problems remain.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58E20, 53C20, 58D15

Retrieve articles in all journals with MSC: 58E20, 53C20, 58D15

Additional Information

PII: S 0002-9947(1979)0539921-1
Article copyright: © Copyright 1979 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia