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Books on the topic 'Riemannian manifolds'

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Author: Grafiati

Published: 4 June 2021

Last updated: 31 July 2024

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1

Lee, John M. Riemannian Manifolds. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/b98852.

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2

Lee, John M. Introduction to Riemannian Manifolds. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91755-9.

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3

Tondeur, Philippe. Foliations on Riemannian Manifolds. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4613-8780-0.

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4

Lang, Serge, ed. Differential and Riemannian Manifolds. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4182-9.

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5

Tondeur, Philippe. Foliations on Riemannian manifolds. New York: Springer-Verlag, 1988.

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6

Lang, Serge. Differential and Riemannian manifolds. New York: Springer-Verlag, 1995.

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7

Hebey, Emmanuel. Sobolev Spaces on Riemannian Manifolds. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0092907.

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8

Berestovskii, Valerii, and Yurii Nikonorov. Riemannian Manifolds and Homogeneous Geodesics. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56658-6.

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9

Min, Ji. Minimal surfaces in Riemannian manifolds. Providence, R.I: American Mathematical Society, 1993.

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10

Hebey, Emmanuel. Sobolev spaces on Riemannian manifolds. Berlin: Springer-Verlag, 1996.

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11

Ritoré, Manuel. Isoperimetric Inequalities in Riemannian Manifolds. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-37901-7.

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12

C, Wood John, ed. Harmonic morphisms between Riemannian manifolds. Oxford: Clarendon Press, 2003.

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13

Fong, Robert Simon, and Peter Tino. Population-Based Optimization on Riemannian Manifolds. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04293-5.

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14

Duggal, Krishan L., and Ramesh Sharma. Symmetries of Spacetimes and Riemannian Manifolds. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-5315-1.

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15

Shiohama, Katsuhiro, Takashi Sakai, and Toshikazu Sunada, eds. Curvature and Topology of Riemannian Manifolds. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075643.

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16

Güneysu, Batu. Covariant Schrödinger Semigroups on Riemannian Manifolds. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68903-6.

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17

Rovenskii, Vladimir Y. Foliations on Riemannian Manifolds and Submanifolds. Boston, MA: Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-4270-3.

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18

García-Río, Eduardo, Demir N. Kupeli, and Ramón Vázquez-Lorenzo. Osserman Manifolds in Semi-Riemannian Geometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/b83213.

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19

Duggal, Krishan L. Symmetries of spacetimes and Riemannian manifolds. Dordrecht: Kluwer Academic Publishers, 1999.

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20

N, Kupeli Demir, and Vázquez-Lorenzo Ramón, eds. Osserman manifolds in semi-Riemannian geometry. Berlin: Springer, 2002.

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21

Steven, Rosenberg. The Laplacian on a Riemannian manifold: An introduction to analysis on manifolds. Cambridge, U.K: Cambridge University Press, 1997.

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22

Krzysztof, Galicki, Simanca S. R, and Boyer Charles P, eds. Riemannian topology and geometric structures on manifolds. Boston [Mass.]: Birkhäuser, 2009.

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23

1945-, Pastore Anna Maria, and Ianuș Stere, eds. Riemannian submersions and related topics. Singapore: World Scientific, 2004.

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24

Leonidovich, Verner Alekseĭ, and Leningradskiĭ gosudarstvennyĭ pedagogicheskiĭ institut imeni A.I. Gert͡s︡ena., eds. Issledovanii͡a︡ po teorii rimanovykh mnogoobraziĭ i ikh pogruzheniĭ: Mezhvuzovskiĭ sbornik nauchnykh trudov. Leningrad: Leningradskiĭ gos. pedagog. in-t im. A.I. Gert͡s︡ena, 1985.

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25

Obata, Wakako. Homogeneous Kähler Einstein manifolds of nonpositive curvature operator. Sendai, Japan: Tohoku University, 2007.

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26

Galicki, Krzysztof, and Santiago R. Simanca, eds. Riemannian Topology and Geometric Structures on Manifolds. Boston, MA: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4743-8.

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27

Blair, David E. Riemannian Geometry of Contact and Symplectic Manifolds. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4959-3.

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28

Blair, David E. Riemannian Geometry of Contact and Symplectic Manifolds. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4757-3604-5.

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29

Kangaslampi, Riikka. Uniformly quasiregular mappings on elliptic Riemannian manifolds. Helsinki: Suomalainen Tiedeakatemia, 2008.

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30

1954-, Baum Helga, ed. Twistors and killing spinors on Riemannian manifolds. Stuttgart: Teubner, 1991.

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31

Deruelle, Nathalie, and Jean-Philippe Uzan. Riemannian manifolds. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0042.

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This chapter introduces the Riemann tensor characterizing curved spacetimes, and then the metric tensor, which allows lengths and durations to be defined. As shown in the preceding chapter, ‘absolute, true, and mathematical’ spacetimes representing ‘relative, apparent, and common’ space and time in Einstein’s theory are Riemannian manifolds supplied with a metric and its associated Levi-Civita connection. Moreover, this metric simultaneously describes the coordinate system chosen to reference the events. The chapter begins with a study of connections, parallel transport, and curvature; the commutation of derivatives, torsion, and curvature; geodesic deviation and curvature; the metric tensor and the Levi-Civita connection; and locally inertial frames. Finally, it discusses Riemannian manifolds.

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32

Deruelle, Nathalie, and Jean-Philippe Uzan. Riemannian manifolds. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0064.

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This chapter is about Riemannian manifolds. It first discusses the metric manifold and the Levi-Civita connection, determining if the metric is Riemannian or Lorentzian. Next, the chapter turns to the properties of the curvature tensor. It states without proof the intrinsic versions of the properties of the Riemann–Christoffel tensor of a covariant derivative already given in Chapter 2. This chapter then performs the same derivation as in Chapter 4 by obtaining the Einstein equations of general relativity by varying the Hilbert action. However, this will be done in the intrinsic manner, using the tools developed in the present and the preceding chapters.

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33

Lee, John M. Riemannian Manifolds. Island Press, 1997.

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34

Lee, John M. Introduction to Riemannian Manifolds. Springer, 2019.

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35

Foliations on Riemannian Manifolds. Springer, 2011.

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36

Introduction to Riemannian Manifolds. Springer International Publishing AG, 2021.

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37

Tondeur, Philippe. Foliations on Riemannian Manifolds. Springer, 2012.

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38

Lang, Serge. Differential and Riemannian Manifolds. Island Press, 1995.

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39

Lang, Serge. Differential and Riemannian Manifolds. Springer New York, 2012.

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40

Lang, Serge. Differential and Riemannian Manifolds. Springer London, Limited, 2012.

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41

Molino, Pierre. Riemannian Foliations. Springer, 2012.

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42

Riemannian foliations. Boston: Birkhäuser, 1988.

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43

Berestovskii, Valerii, and Yurii Nikonorov. Riemannian Manifolds and Homogeneous Geodesics. Springer International Publishing AG, 2021.

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44

Geometric Mechanics on Riemannian Manifolds. Boston: Birkhäuser-Verlag, 2005. http://dx.doi.org/10.1007/b138771.

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45

Calin, Ovidiu, and Der-Chen Chang. Geometric Mechanics on Riemannian Manifolds. Springer, 2009.

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46

Riemannian Manifolds of Conullity Two. World Scientific Publishing Co Pte Ltd, 1996.

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47

Tricerri, F., and L. Vanhecke. Homogeneous Structures on Riemannian Manifolds. Cambridge University Press, 2013.

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48

Berestovskii, Valerii N., and Yurii Nikonorov. Riemannian Manifolds and Homogeneous Geodesics. Springer International Publishing AG, 2020.

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49

Hebey, Emmanuel. Sobolev Spaces on Riemannian Manifolds. Springer London, Limited, 2006.

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50

Blair, D. E. Contact Manifolds in Riemannian Geometry. Springer London, Limited, 2006.

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