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Structures on Manifolds

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter begins by introducing various geometries that play important roles in the way they relate to Sasakian structures. It espouses the point of view that a geometric structure is best ... More


Introduction to Kähler Manifolds

Eduardo Cattani and Phillip Griffiths

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, Lê Dũng Tráng, Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng (eds)

in Hodge Theory (MN-49)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161341
eISBN:
9781400851478
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161341.003.0001
Subject:
Mathematics, Geometry / Topology

This chapter provides an introduction to the basic results on the topology of compact Kähler manifolds that underlie and motivate Hodge theory. This chapter consists of five sections which ... More


Poisson and symplectic manifolds

S. G. Rajeev

in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.003.0014
Subject:
Physics, Atomic, Laser, and Optical Physics

The Poisson bracket defines a tensor on the phase space which satisfies an integrability condition. When this tensor is invertible, this condition is linear and gives a symplectic structure. ... More


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