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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Scalar curvature, inequality and submanifold


Authors: Bang-yen Chen and Masafumi Okumura
Journal: Proc. Amer. Math. Soc. 38 (1973), 605-608
MSC: Primary 53C40
MathSciNet review: 0343217
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Abstract: Using an inequality relation between scalar curvature and length of second fundamental form, we may conclude that a submanifold must have nonnegative (or positive) sectional curvatures. An application to compact submanifolds in obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0343217-0
Keywords: Scalar curvature, length of second fundamental form, sectional curvature, parallel normal vector field, minimal submanifold
Article copyright: © Copyright 1973 American Mathematical Society