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- W2945823032 abstract "In this note, we investigate conformally flat submanifolds of Euclidean space with positive index of relative nullity. Let $M^n$ be a complete conformally flat manifold and let $fcolon M^nto R^m$ be an isometric immersion. We prove the following results: (1) If the index of relative nullity is at least two, then $M^n$ is flat and $f$ is a cylinder over a flat submanifold. (2) If the scalar curvature of $M^n$ is non-negative and the index of relative nullity is positive, then $f$ is a cylinder over a submanifold with constant non-negative sectional curvature. (3) If the scalar curvature of $M^n$ is non-zero and the index of relative nullity is constant and equal to one, then $f$ is a cylinder over a $(n-1)$-dimensional submanifold with non-zero constant sectional curvature." @default.
- W2945823032 created "2019-05-29" @default.
- W2945823032 creator A5025884255 @default.
- W2945823032 date "2019-05-22" @default.
- W2945823032 modified "2023-09-27" @default.
- W2945823032 title "On Complete Conformally flat submanifolds with nullity in Euclidean space" @default.
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