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A note on the first Betti number of submanifolds with nonnegative Ricci curvature in codimension two

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Abstract

We show that a complete submanifold in codimension two with nonnegative Ricci curvature which contains no lines and is covered by\(\bar M \times R\) has nonnegative sectional curvatures. This implies some results about the first Betti number of such a submanifold.

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Authors and Affiliations

  1. Department of Mathematics, California State University, Northridge, 91330, Northridge, CA, USA

    Maria Helena Noronha

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  1. Maria Helena Noronha
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Noronha, M.H. A note on the first Betti number of submanifolds with nonnegative Ricci curvature in codimension two. Manuscripta Math 73, 335–339 (1991). https://doi.org/10.1007/BF02567645

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  • DOI: https://doi.org/10.1007/BF02567645

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