Riemannian submersions with minimal fibers and affine hypersurfaces |
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Authors: | Bang-Yen Chen |
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Affiliation: | (1) Michigan State University, East Lansing, MI, USA |
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Abstract: | Let π : M → B be a Riemannian submersion with minimal fibers. In this article we prove the following results: (1) If M is positively curved, then the horizontal distribution of the submersion is a non-totally geodesic distribution; (2) if M is non-negatively (respectively, negatively) curved, then the fibers of the submersion have non-positive (respectively, negative) scalar curvature; and (3) if M can be realized either as an elliptic proper centroaffine hypersphere or as an improper hypersphere in some affine space, then the horizontal distribution is non-totally geodesic. Several applications are also presented. |
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Keywords: | 2000 Mathematics Subject Classification: 53C40 53C42 53B25 |
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