## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Riemannian submersions, minimal immersions and cohomology class

Bang-Yen Chen

#### Abstract

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

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

Dates
First available in Project Euclid: 28 December 2005

https://projecteuclid.org/euclid.pja/1135791768

Digital Object Identifier
doi:10.3792/pjaa.81.162

Mathematical Reviews number (MathSciNet)
MR2196721

Zentralblatt MATH identifier
1147.53312

#### Citation

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. https://projecteuclid.org/euclid.pja/1135791768

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