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Books on the topic 'Riemannian metric and distance'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Gromov, Mikhael. Metric structures for Riemannian and non-Riemannian spaces. Birkhäuser, 1999.

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2

Grove, Karsten. Riemannian geometry: A metric entrance. University of Aarhus, Dept. of Mathemtics, 1999.

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3

1954-, Walschap Gerard, and SpringerLink (Online service), eds. Metric foliations and curvature. Birkhäuser, 2009.

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4

Washington, Allyn J. Basic technical mathematics with calculus. 5th ed. Addison-Wesley, 1990.

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5

Washington, Allyn J. Basic technical mathematics with calculus. 8th ed. Pearson/Addison-Wesley, 2005.

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6

Washington, Allyn J. Basic technical mathematics with calculus. 6th ed. Addison-Wesley, 1995.

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Washington, Allyn J. Basic technical mathematics with calculus. 5th ed. Benjamin/Cummings Pub. Co., 1990.

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8

Washington, Allyn J. Basic technical mathematics with calculus. 7th ed. Addison-Wesley, 2000.

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9

Washington, Allyn J. Basic technical mathematics with calculus. 4th ed. Benjamin/Cummings Pub. Co., 1985.

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10

Washington, Allyn J. Basic technical mathematics with calculus. 4th ed. Benjamin/Cummings Pub. Co., 1985.

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11

author, Tian Gang 1958, ed. The geometrization conjecture. American Mathematical Society, 2014.

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12

Metric Structures for Riemannian and Non-Riemannian Spaces. Birkhäuser Boston, 2007. http://dx.doi.org/10.1007/978-0-8176-4583-0.

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13

LaFontaine, Jacques. Metric Structures for Riemannian and Non-Riemannian Spaces. Birkhäuser Boston, 2010.

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14

Metric structures for Riemannian and non-Riemannian spaces. Birkhäuser, 2007.

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15

Walczak, Szymon M. Metric Diffusion along Foliations. Springer International Publishing AG, 2017.

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16

Gromov, Mikhail, M. Katz, S. Semmes, and P. Pansu. Metric Structures for Riemannian and Non-Riemannian Spaces (Modern Birkhäuser Classics). Birkhäuser Boston, 2006.

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17

Moduli Spaces of Riemannian Metrics. Birkhauser, 2015.

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18

Tuschmann, Wilderich, and David J. Wraith. Moduli Spaces of Riemannian Metrics. Birkhauser Verlag, 2015.

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19

Gromov, Misha. Metric Structures for Riemannian and Non-Riemannian Spaces (Progress in Materials Science). Birkhauser Verlag AG, 1998.

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20

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 com

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21

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

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22

Gromov, Mikhail, M. Katz, and S. Semmes. Metric Structures for Riemannian and Non-Riemannian Spaces: Based on Structures Metriques des Varietes Riemanniennes (Progress in Mathematics). Birkhäuser Boston, 2001.

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23

Sullivan, Navin. Area, Distance, And Volume (Measure Up!). Benchmark Books (NY), 2006.

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24

O'Donnell, Kerri. Natural Wonders of the World: Converting Distance Measurements to Metric Units. Rosen Publishing Group, 2004.

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25

Natural Wonders of the World: Converting Distance Measurements to Metric Units. Rosen Publishing Group, 2009.

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26

O'Donnell, Kerri. Natural Wonders of the World: Converting Distance Measurements to Metric Units. Rosen Publishing Group, 2005.

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27

Adams, Rebecca Ann. History of metrization, 1905-1951. 1992.

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28

Natural Wonders of the World: Converting Distance Measurements to Metric Units. Rosen Publishing Group, 2009.

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29

Natural Wonders of the World: Converting Distance Measurements to Metric Units. Rosen Publishing Group, 2009.

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30

Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance. American Mathematical Society, 2004.

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31

Rakočević, Vladimir. Fixed Point Results in W-Distance Spaces. Taylor & Francis Group, 2021.

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32

Fixed Point Results in W-Distance Spaces. Taylor & Francis Group, 2021.

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33

Gollin, Edward, and Alexander Rehding, eds. The Oxford Handbook of Neo-Riemannian Music Theories. Oxford University Press, 2011. http://dx.doi.org/10.1093/oxfordhb/9780195321333.001.0001.

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In recent years Hugo Riemann's ideas have thoroughly captured the music-theoretical imagination, both in the United States and abroad. Neo-Riemannian theory has proven particularly adept at explaining features of chromatic music where other theoretical approaches have failed, and thereby established itself as the leading theoretical approach of our time. This book brings together a group of proponents of Riemannian and neo-Riemannian theory for an exploration of the music-analytical, systematic, and historical aspects of this new field. It elucidates key aspects of the field, draws connections

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34

Rajeev, S. G. Curvature and Instability. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0011.

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The Euler equations of a rigid body can be understood as the geodesic equations for a metric on the rotation group. A rapid introduction to the Riemannian geometry of Lie groups (following Milnor) is given and illuminated by the example of the rigid body. The deep generalization of Arnold to the case of an incompressible fluid is then explained. The Euler equations of an ideal incompressible fluid are shown to be geodesics of the group of volume preserving diffeomorphisms. The curvature of this metric is calculated. Contrary to the case of the rigid body, the curvature is negative, implying th

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35

Street, Brian. The Calder´on-Zygmund Theory II: Maximal Hypoellipticity. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691162515.003.0002.

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This chapter remains in the single-parameter case and turns to the case when the metric is a Carnot–Carathéodory (or sub-Riemannian) metric. It defines a class of singular integral operators adapted to this metric. The chapter has two major themes. The first is a more general reprise of the trichotomy described in Chapter 1 (Theorem 2.0.29). The second theme is a generalization of the fact that Euclidean singular integral operators are closely related to elliptic partial differential equations. The chapter also introduces a quantitative version of the classical Frobenius theorem from different

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36

Deruelle, Nathalie, and Jean-Philippe Uzan. The Cartan structure equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0065.

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This chapter focuses on Cartan structure equations. It first introduces a 1-form and its exterior derivative, before turning to a study of the connection and torsion forms, thereby expressing the torsion as a function of the connection forms and establishing the torsion differential 2-forms. It then turns to the curvature forms drawn from Chapter 23 and Cartan’s second structure equation, along with the curvature 2-forms. It also studies the Levi-Civita connection. The components of the Riemann tensor are then studied, with a Riemannian manifold, or a metric manifold with a torsion-less connec

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37

Mashhoon, Bahram. Extension of General Relativity. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803805.003.0005.

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Nonlocal general relativity (GR) requires an extension of the mathematical framework of GR. Nonlocal GR is a tetrad theory such that the orthonormal tetrad frame field of a preferred set of observers carries the sixteen gravitational degrees of freedom. The spacetime metric is then defined via the orthonormality condition. The preferred frame field is used to define a new linear Weitzenböck connection in spacetime. The non-symmetric Weitzenböck connection is metric compatible, curvature-free and renders the preferred (fundamental) frame field parallel. This circumstance leads to teleparallelis

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38

Tretkoff, Paula. Riemann Surfaces, Coverings, and Hypergeometric Functions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0003.

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This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and notes that an automorphism of a Riemann surface is a biholomorphic map of the Riemann surface onto itself. It then describes a Riemannian metric and the Gauss-Bonnet theorem, which can be interpreted as a relation between the Gaussian curvature of a compact Riemann surface X and its Euler characteristic. It also examines the behavior of the Euler number under finite covering, along with finite subgroup

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39

Wittman, David M. Spacetime Geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199658633.003.0011.

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This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meani

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40

Saha, Prasenjit, and Paul A. Taylor. The Expanding Universe. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816461.003.0008.

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This chapter covers the now generally accepted ‘concordance model’ of the Universe, along with a few other historical models that were leading candidates previously. The theoretical underpinnings of the Cosmological Principle and its observational evidence are presented. The formalism of the Friedmann equation and the Robertson–Walker metric are introduced (without derivation), and the key concepts of lookback time and comoving distance are explained. The different mass–energy constituents in the concordance cosmology (including curvature, dark matter, and dark energy) are also described, alon

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41

Goliszek, Sławomir. Znaczenie komponentów dostępności transportowej w Szczecinie w latach 2009-2018 = Significance of transport acces-sibility components in Szczecin in the period 2009-2018. Instytut Geografii i Przestrzennego Zagospodarowania im. Stanisława Leszczyckiego, Polska Akademia Nauk, 2022. http://dx.doi.org/10.7163/9788361590910.

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This monograph deals with the importance of the components of transport accessibility in the city of Szczecin, north-western Poland, over the period 2009-2018, with particular attention to public transport. The study uses census districts to look at the accessibility of a range of destinations by both public and private (car) means of transport in 2018 and adds three other years, 2009, 2012 and 2015, for public transport alone. The empirical part of the study involved statistical methods and specific points in time in 2018, including date, hour and minute. The specific metrics used for the sta

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