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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Hypersurfaces in space forms satisfying the condition $\Delta x=Ax+B$
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by Luis J. Alías, Angel Ferrández and Pascual Lucas PDF
Trans. Amer. Math. Soc. 347 (1995), 1793-1801 Request permission

Abstract:

In this work we study and classify pseudo-Riemannian hypersurfaces in pseudo-Riemannian space forms which satisfy the condition $\Delta x = Ax + B$, where $A$ is an endomorphism, $B$ is a constant vector, and $x$ stands for the isometric immersion. We prove that the family of such hypersurfaces consists of open pieces of minimal hypersurfaces, totally umbilical hypersurfaces, products of two nonflat totally umbilical submanifolds, and a special class of quadratic hypersurfaces.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1793-1801
  • MSC: Primary 53C40; Secondary 53C42, 53C50
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1257095-8
  • MathSciNet review: 1257095