Lie Groups and Lie Algebras
In this chapter, we recall some well-known results on Lie groups and Lie algebras. In particular, we discuss the third Lie theorem, the Ado theorem, and the Cartan semisimplicity criterion. Some important types of Lie algebras and Lie groups together with
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Valerii Berestovskii Yurii Nikonorov
Riemannian Manifolds and Homogeneous Geodesics
Springer Monographs in Mathematics Editors-in-Chief Isabelle Gallagher, Département de Mathématiques et Applications, Ecole Normale Supérieure, Paris, France Minhyong Kim, School of Mathematics, Korea Institute for Advanced Study, Seoul, South Korea; Mathematical Institute, University of Warwick, Coventry, UK Series Editors Sheldon Axler, Department of Mathematics, San Francisco State University, San Francisco, CA, USA Mark Braverman, Department of Mathematics, Princeton University, Princeton, NJ, USA Maria Chudnovsky, Department of Mathematics, Princeton University, Princeton, NJ, USA Tadahisa Funaki, Department of Mathematics, University of Tokyo, Tokyo, Japan Sinan Güntürk, Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY, USA Claude Le Bris, CERMICS, Ecole des Ponts ParisTech, Marne la Vallée, France Pascal Massart, Département de Mathématiques, Université de Paris-Sud, Orsay, France Alberto A. Pinto, Department of Mathematics, University of Porto, Porto, Portugal Gabriella Pinzari, Department of Mathematics, University of Padova, Padova, Italy Ken Ribet, Department of Mathematics, University of California, Berkeley, CA, USA René Schilling, Institut für Mathematische Stochastik, Technische Universität Dresden, Dresden, Germany Panagiotis Souganidis, Department of Mathematics, University of Chicago, Chicago, IL, USA Endre Süli, Mathematical Institute, University of Oxford, Oxford, UK Shmuel Weinberger, Department of Mathematics, University of Chicago, Chicago, IL, USA Boris Zilber, Mathematical Institute, University of Oxford, Oxford, UK
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Valerii Berestovskii Yurii Nikonorov •
Riemannian Manifolds and Homogeneous Geodesics
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Valerii Berestovskii Sobolev Institute of Mathematics Siberian Branch of the Russian Academy of Sciences Novosibirsk, Russia
Yurii Nikonorov Southern Mathematical Institute Scientific Centre of the Russian Academy of Sciences Vladikavkaz, Russia
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-030-56657-9 ISBN 978-3-030-56658-6 (eBook) https://doi.org/10.1007/978-3-030-56658-6 Mathematics Subject Classification: 53C30, 53C22, 53C20, 53B21, 22F30, 22E60, 22E15 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights
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