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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, Number 8, Pages 69–78 (Mi ivm8920)  

This article is cited in 1 scientific paper (total in 1 paper)

First nonzero eigenvalue of a pseudo-umbilical hypersurface in the unit sphere

Majid Ali Choudhary

Department of Mathematics, Jamia Millia Islamia, Jamia Nagar, New Delhi, 110025 India
Full-text PDF (188 kB) Citations (1)
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Abstract: S. Deshmukh has obtained interesting results for first nonzero eigenvalue of a minimal hypersurface in the unit sphere. In the present article, we generalize these results to pseudo-umbilical hypersurface and prove: what conditions are satisfied by the first nonzero eigenvalue $\lambda_1$ of the Laplacian operator on a compact immersed pseudo-umbilical hypersurface $M$ in the unit sphere $S^{n+1}$. We also show that a compact immersed pseudo-umbilical hypersurface of the unit sphere $S^{n+1}$ with $\lambda_1=n$ is either isometric to the sphere $S^n$ or for this hypersurface an inequality is fulfilled in which sectional curvatures of the hypersuface $M$ participate.
Keywords: pseudoumbilical hypersurface, eigenvalue of Laplacian operator.
Received: 24.01.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, Volume 58, Issue 8, Pages 56–64
DOI: https://doi.org/10.3103/S1066369X14080076
Bibliographic databases:
Document Type: Article
UDC: 514.763
Language: Russian
Citation: Majid Ali Choudhary, “First nonzero eigenvalue of a pseudo-umbilical hypersurface in the unit sphere”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 8, 69–78; Russian Math. (Iz. VUZ), 58:8 (2014), 56–64
Citation in format AMSBIB
\Bibitem{Maj14}
\by Majid Ali Choudhary
\paper First nonzero eigenvalue of a~pseudo-umbilical hypersurface in the unit sphere
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 8
\pages 69--78
\mathnet{http://mi.mathnet.ru/ivm8920}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 8
\pages 56--64
\crossref{https://doi.org/10.3103/S1066369X14080076}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84904608516}
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  • https://www.mathnet.ru/eng/ivm8920
  • https://www.mathnet.ru/eng/ivm/y2014/i8/p69
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Full-text PDF :45
    References:42
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