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Publication list for Clelland, Jeanne

  • From Frenet to Cartan: The Method of Moving Frames
    Base Product Code Keyword List: gsm; GSM; gsm/178; GSM/178; gsm-178; GSM-178
    Print Product Code: GSM/178
    Online Product Code: GSM/178.E
    Title (HTML): From Frenet to Cartan: The Method of Moving Frames
    Author(s) (Product display): Jeanne N. Clelland
    Affiliation(s) (HTML): University of Colorado, Boulder, CO

    The method of moving frames originated in the early nineteenth century with the notion of the Frenet frame along a curve in Euclidean space. Later, Darboux expanded this idea to the study of surfaces. The method was brought to its full power in the early twentieth century by Elie Cartan, and its development continues today with the work of Fels, Olver, and others.

    This book is an introduction to the method of moving frames as developed by Cartan, at a level suitable for beginning graduate students familiar with the geometry of curves and surfaces in Euclidean space. The main focus is on the use of this method to compute local geometric invariants for curves and surfaces in various 3-dimensional homogeneous spaces, including Euclidean, Minkowski, equi-affine, and projective spaces. Later chapters include applications to several classical problems in differential geometry, as well as an introduction to the nonhomogeneous case via moving frames on Riemannian manifolds.

    The book is written in a reader-friendly style, building on already familiar concepts from curves and surfaces in Euclidean space. A special feature of this book is the inclusion of detailed guidance regarding the use of the computer algebra system Maple™ to perform many of the computations involved in the exercises.

    An excellent and unique graduate level exposition of the differential geometry of curves, surfaces and higher-dimensional submanifolds of homogeneous spaces based on the powerful and elegant method of moving frames. The treatment is self-contained and illustrated through a large number of examples and exercises, augmented by Maple code to assist in both concrete calculations and plotting. Highly recommended.

    Niky Kamran, McGill University

    The method of moving frames has seen a tremendous explosion of research activity in recent years, expanding into many new areas of applications, from computer vision to the calculus of variations to geometric partial differential equations to geometric numerical integration schemes to classical invariant theory to integrable systems to infinite-dimensional Lie pseudo-groups and beyond. Cartan theory remains a touchstone in modern differential geometry, and Clelland's book provides a fine new introduction that includes both classic and contemporary geometric developments and is supplemented by Maple symbolic software routines that enable the reader to both tackle the exercises and delve further into this fascinating and important field of contemporary mathematics.

    Recommended for students and researchers wishing to expand their geometric horizons.

    Peter Olver, University of Minnesota

    Book Series Name: Graduate Studies in Mathematics
    Volume: 178
    Publication Month and Year: 2017-03-29
    Copyright Year: 2017
    Page Count: 414
    Cover Type: Hardcover
    Print ISBN-13: 978-1-4704-2952-2
    Online ISBN 13: 978-1-4704-3747-3
    Print ISSN: 1065-7339
    Online ISSN: 1065-7339
    Primary MSC: 22; 53; 58
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    Applied Math?: false
    MAA Book?: false
    Home Page?: false
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    Reference?: false
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    Apparel or Gift: false
    SXG Subject: GT
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-178
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    Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3747-3&pisbn=978-1-4704-2952-2&epc=GSM/178.E&ppc=GSM/178&title=From%20Frenet%20to%20Cartan%3A%20The%20Method%20of%20Moving%20Frames&author=Jeanne%20N.%20Clelland&type=DE
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3747-3&pisbn=978-1-4704-2952-2&epc=GSM/178.E&ppc=GSM/178&title=From%20Frenet%20to%20Cartan%3A%20The%20Method%20of%20Moving%20Frames&author=Jeanne%20N.%20Clelland&type=R

    Undergraduate and graduate students interested in differential geometry.


    The present book has a high didactical and scientific quality being a very careful introduction to the method of moving frames...this book is a very nice presentation of an essential tool of classical differential geometry. I strongly recommend it as a welcome addition to the main textbooks in geometry.

    -- Mircea Crâşmăreanu, Zentralblatt MATH

    This volume provides a well-written and accessible introduction to Cartan's theory of moving frames for curves and surfaces in several 3-dimensional geometries.

    -- Francis Valiquette, Mathematical Reviews

    Primarily intended for 'beginning graduate students,' this book is highly recommended to anyone seeking to extend their knowledge of differential geometry beyond the undergraduate level.

    -- Peter Ruane, MAA Reviews

    Related Products: Cartan for Beginners Curves and Surfaces
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