Proceedings of the Japan Academy, Series A, Mathematical Sciences

Riemannian submersions, minimal immersions and cohomology class

Bang-Yen Chen

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We prove a simple optimal relationship between Riemannian submersions and minimal immersions; namely, if a Riemannian manifold admits a non-trivial Riemannian submersion with totally geodesic fibers, then it cannot be isometrically immersed in any Riemannian manifold of non-positive sectional curvature as a minimal manifold. Some related results are also presented. In the last section, we introduce a cohomology class for Riemannian submersions and provide an application.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 10 (2005), 162-167.

First available in Project Euclid: 28 December 2005

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Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32]

Riemannian submersion minimal immersion cohomology class totally geodesic fibers


Chen, Bang-Yen. Riemannian submersions, minimal immersions and cohomology class. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 10, 162--167. doi:10.3792/pjaa.81.162.

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