Basic Concepts of Riemannian Geometry
In this first, introductory chapter we recall some important definitions and results of Riemannian Geometry, essentially following [1]. Although we assume the reader to be familiar with the general subject, as presented, e.g., in the standard references [
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Giovanni Catino Paolo Mastrolia
A Perspective on Canonical Riemannian Metrics Ferran Sunyer i Balaguer Award Winning monograph
Progress in Mathematics Volume 336
Series Editors Antoine Chambert-Loir, Université Paris-Diderot, Paris, France Jiang-Hua Lu, The University of Hong Kong, Hong Kong SAR, China Michael Ruzhansky, Ghent University, Belgium and Queen Mary University of London, UK Yuri Tschinkel, Courant Institute of Mathematical Sciences, New York, USA
More information about this series at http://www.springer.com/series/4848
Giovanni Catino • Paolo Mastrolia
A Perspective on Canonical Riemannian Metrics
Giovanni Catino Dipartimento di Matematica Politecnico di Milano Milano, Italy
Paolo Mastrolia Dipartimento di Matematica Università degli Studi di Milano Milano, Italy
ISSN 0743-1643 ISSN 2296-505X (electronic) Progress in Mathematics ISBN 978-3-030-57184-9 ISBN 978-3-030-57185-6 (eBook) https://doi.org/10.1007/978-3-030-57185-6 Mathematics Subject Classification (2010): 53C25, 53C20, 53C21 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Ferran Sunyer i Balaguer (1912–1967) was a selftaught Catalan mathematician who, in spite of a serious physical disability, was very active in research in classical mathematical analysis, an area in which he acquired international recognition. His heirs created the Fundaci´o Ferran Sunyer i Balaguer inside the Institut d’Estudis Catalans to honor the memory of Ferran Sunyer i Balaguer and to promote mathematical research. Each year, the Fundaci´o Ferran Sunyer
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