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A ladder of curvatures for hypersurfaces in the Euclidean ambient space

Brzycki, Bryan and Giesler, Matthew D. and Gomez, Kevin and Odom, Lucy H. and Suceavă, Bogdan D. (2014) A ladder of curvatures for hypersurfaces in the Euclidean ambient space. Houston Journal of Mathematics, 40 (4). pp. 1347-1356. ISSN 0362-1588. http://resolver.caltech.edu/CaltechAUTHORS:20150219-110203852

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Abstract

We introduce a string of new curvature invariants of a hypersurface in the real (n + 1)-dimensional space and we establish a ladder of inequalities involving these curvature invariants. There is an analogy between this series of inequalities and the classical ladder of power means for positive real numbers. To describe the natural geometric interpretation of our proposed construction we refer to B. Riemann's original idea of sectional curvature.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://www.math.uh.edu/~hjm/Vol40-4.htmlPublisherArticle
Additional Information:© 2014 University of Houston. Communicated by David Bao Dedicated to Dr. Bang-Yen Chen's Seventieth Birthday. Received September 16, 2013.
Group:TAPIR
Subject Keywords:Principal curvatures, sectional curvature, scalar curvature, shape operator, absolutely umbilical hypersurfaces, ladder of power means, inequalities with real numbers.
Classification Code:2010 MSC: 53B25, 53B20, 53A30
Record Number:CaltechAUTHORS:20150219-110203852
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150219-110203852
Official Citation:Bryan Brzycki, Kevin Gomez, and Bogdan D. Suceavă, Department of Mathematics, California State University, Fullerton, CA 91834-6850, U.S.A, (bryan6brzycki@gmail.com), (kgomez81@csu.fullerton.edu), (bsuceava@fullerton.edu), Matthew D. Giesler, California Institute of Technology, TAPIR 350-17, 1200 E. California Boulevard, Pasadena, CA 91125-0001, U.S.A. (mgiesler@caltech.edu), and Lucy H. Odom, Department of Mathematics, San Francisco State University, 1600 Holloway Ave, San Francisco, CA 94132, U.S.A. (lodom@mail.sfsu.edu). A ladder of curvatures for hypersurfaces in the Euclidean ambient space, pp. 1347-1356.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55007
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:19 Feb 2015 20:40
Last Modified:19 Feb 2015 20:40

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