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Books on the topic 'Riemannian symmetric spaces'

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Author: Grafiati
Published: 8 June 2024

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1

Flensted-Jensen, Mogens. Analysis on non-Riemannian symmetric spaces. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1986.

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2

Burstall, Francis E., and John H. Rawnsley. Twistor Theory for Riemannian Symmetric Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0095561.

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3

Borel, Armand. Semisimple Groups and Riemannian Symmetric Spaces. Gurgaon: Hindustan Book Agency, 1998. http://dx.doi.org/10.1007/978-93-80250-92-2.

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4

Helgason, Sigurdur. Geometric analysis on symmetric spaces. 2nd ed. Providence, R.I: American Mathematical Society, 2008.

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5

Helgason, Sigurdur. Geometric analysis on symmetric spaces. Providence, R.I: American Mathematical Society, 1994.

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6

Kauffman, R. M. Eigenfunction expansions, operator algebras, and Riemannian symmetric spaces. Harlow, Essex, England: Addison Longman Ltd., 1996.

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7

Burstall, Francis E. Twistor theory for Riemannian symmetric spaces: With applications to harmonic maps of Riemann surfaces. Berlin: Springer-Verlag, 1990.

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8

Werner, Müller. L²-index of elliptic operators on manifolds with cusps of rank one. Berlin: Akademie der Wissenschaften der DDR, Karl-Weierstrass-Institut für Mathematik, 1985.

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9

Krotz, Bernhard. The emage of the heat kernel transform fon Riemannian symmetric spaces of the noncompact type. Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2005.

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10

Wolf, Joseph Albert. Spaces of constant curvature. 6th ed. Providence, R.I: AMS Chelsea Pub., 2011.

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11

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

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12

Borel, Armand. Semisimple Groups and Riemannian Symmetric Spaces. Hindustan Book Agency, 2011.

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13

Boeckx, Eric, Oldrich Kowalski, and Lieven Vanhecke. Riemannian Manifolds of Conullity Two. World Scientific Pub Co Inc, 1996.

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14

Rawnsley, John H., and Francis E. Burstall. Twister Theory for Riemannian Symmetric Spaces (Lecture Notes in Mathematics, Vol 1424). Springer, 1990.

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15

Zirnbauer, Martin R. Symmetry classes. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.3.

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Abstract:
This article examines the notion of ‘symmetry class’, which expresses the relevance of symmetries as an organizational principle. In his 1962 paper The threefold way: algebraic structure of symmetry groups and ensembles in quantum mechanics, Dyson introduced the prime classification of random matrix ensembles based on a quantum mechanical setting with symmetries. He described three types of independent irreducible ensembles: complex Hermitian, real symmetric, and quaternion self-dual. This article first reviews Dyson’s threefold way from a modern perspective before considering a minimal extension of his setting to incorporate the physics of chiral Dirac fermions and disordered superconductors. In this minimally extended setting, Hilbert space is replaced by Fock space equipped with the anti-unitary operation of particle-hole conjugation, and symmetry classes are in one-to-one correspondence with the large families of Riemannian symmetric spaces.
16

Rawnsley, John H., and Francis E. Burstall. Twistor Theory for Riemannian Symmetric Spaces: With Applications to Harmonic Maps of Riemann Surfaces. Springer, 2014.

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17

Rawnsley, John H., and Francis E. Burstall. Twistor Theory for Riemannian Symmetric Spaces: With Applications to Harmonic Maps of Riemann Surfaces. Springer London, Limited, 2006.

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18

Rawnsley, John H., and Francis E. Burstall. Twistor Theory for Riemannian Synmetric Spaces with Applications to Harmonic Maps of Riemann Surfaces. Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1990.

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19

Deruelle, Nathalie, and Jean-Philippe Uzan. Cosmological spacetimes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0057.

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Abstract:
This chapter provides a few examples of representations of the universe on a large scale—a first step in constructing a cosmological model. It first discusses the Copernican principle, which is an approximation/hypothesis about the matter distribution in the observable universe. The chapter then turns to the cosmological principle—a hypothesis about the geometry of the Riemannian spacetime representing the universe, which is assumed to be foliated by 3-spaces labeled by a cosmic time t which are homogeneous and isotropic, that is, ‘maximally symmetric’. After a discussion on maximally symmetric space, this chapter considers spacetimes with homogenous and isotropic sections. Finally, this chapter discusses Milne and de Sitter spacetimes.
20

Kachelriess, Michael. Spacetime symmetries. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0006.

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Abstract:
This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.
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