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

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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.

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DOI:
https://doi.org/10.1090/S0002-9947-1979-0539921-1

Article copyright:
© Copyright 1979
American Mathematical Society