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Books on the topic 'Convergence of Riemannian manifolds'

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Published: 10 March 2023

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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

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

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6

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

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7

Riemannian foliations. Boston: Birkhäuser, 1988.

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8

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

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9

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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10

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

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11

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

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12

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

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13

Riemannian geometry of contact and symplectic manifolds. 2nd ed. New York, NY: Birkhäuser, 2010.

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14

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

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15

Foliations on Riemannian manifolds and submanifolds. Boston: Birkhauser, 1998.

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16

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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17

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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18

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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19

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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20

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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21

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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22

Riemannian manifolds: An introduction to curvature. New York: Springer, 1997.

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23

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

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24

Minimal submanifolds in pseudo-Riemannian geometry. New Jersey: World Scientific, 2011.

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25

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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26

Gestur, Ólafsson, and Schlichtkrull Henrik 1954-, eds. The selected works of Sigurdur Helgason. Providence, R.I: American Mathematical Society, 2009.

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27

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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28

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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29

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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30

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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31

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

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32

Riemannian geometry: A beginner's guide. Boston: Jones and Bartlett Publishers, 1993.

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33

G, Ebin D., and American Mathematical Society, eds. Comparison theorems in riemannian geometry. Providence, R.I: American Mathematical Society, 2008.

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34

Riemannian geometry: A beginner's guide. Wellesley, MA: A.K. Peters, 1998.

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35

Conference Board of the Mathematical Sciences., ed. Prescribing the curvature of a Riemannian manifold. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1985.

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36

Kazdan, Jerry L. Prescribing the curvature of a Riemannian manifold. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1985.

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37

Boyer, Charles P. Sasakian geometry. New York: Oxford University Press, 2007.

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38

Barilari, Davide, Ugo Boscain, and Mario Sigalotti, eds. Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Zuerich, Switzerland: European Mathematical Society Publishing House, 2016. http://dx.doi.org/10.4171/162.

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39

Barilari, Davide, Ugo Boscain, and Mario Sigalotti, eds. Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Zuerich, Switzerland: European Mathematical Society Publishing House, 2016. http://dx.doi.org/10.4171/163.

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40

Udrişte, Constantin. Convex Functions and Optimization Methods on Riemannian Manifolds. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8390-9.

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41

Duggal, Krishan L., and Aurel Bejancu. Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-017-2089-2.

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42

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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43

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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Abstract:

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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44

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

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45

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

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46

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

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47

Foliations on Riemannian Manifolds. Springer, 2011.

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48

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

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49

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

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50

Molino, Pierre. Riemannian Foliations. Springer, 2012.

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