Open Access
Dec. 2005 Riemannian submersions, minimal immersions and cohomology class
Bang-Yen Chen
Proc. Japan Acad. Ser. A Math. Sci. 81(10): 162-167 (Dec. 2005). DOI: 10.3792/pjaa.81.162


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.


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Bang-Yen Chen. "Riemannian submersions, minimal immersions and cohomology class." Proc. Japan Acad. Ser. A Math. Sci. 81 (10) 162 - 167, Dec. 2005.


Published: Dec. 2005
First available in Project Euclid: 28 December 2005

zbMATH: 1147.53312
MathSciNet: MR2196721
Digital Object Identifier: 10.3792/pjaa.81.162

Primary: 53C40
Secondary: 53C12

Keywords: cohomology class , minimal immersion , Riemannian submersion , totally geodesic fibers

Rights: Copyright © 2005 The Japan Academy

Vol.81 • No. 10 • Dec. 2005
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