Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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
Trans. Amer. Math. Soc. 347 (1995), 1793-1801
DOI: https://doi.org/10.1090/S0002-9947-1995-1257095-8

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.
References
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Bibliographic 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