Titlebook: Riemannian Geometry of Contact and Symplectic Manifolds; David E. Blair Book 2010Latest edition Springer Science+Business Media LLC 2010 D

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Associated Metrics,ization. We also discuss the action of symplectic and contact transformations on associated metrics. Some of our discussion is broader, dealing with almost Hermitian and almost contact metric structures. The chapter closes with several examples.

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Sasakian and Cosymplectic Manifolds,lso introduce another important structure tensor, ., which will be useful in the study of non-Sasakian contact metric manifolds. As an additional topic, cosymplectic manifolds will be discussed in some detail. We also give several examples and additional commentary.

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Tangent Bundles and Tangent Sphere Bundles, a more general construction on vector bundles and in Section 4 specialize to the case of the normal bundle of a submanifold. The formalism for the tangent bundle and the tangent sphere bundle is of sufficient importance to warrant its own development, rather than specializing from the vector bundle

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Curvature Functionals on Spaces of Associated Metrics,ct manifolds. Since these spaces are smaller than the space of Riemannian metrics of the same total volume, one expects for the classical curvature functionals weaker but still interesting critical point conditions. Other functionals that depend on the symplectic and contact structures are also cons

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Additional Topics in Complex Geometry,95]. In Section 13.2 we discuss the geometry of the projectivized holomorphic tangent and cotangent bundles. The study of the projectivized holomorphic tangent bundle naturally raises the question of a complex geodesic flow, which we discuss in Section 13.3. In Section 13.4 we return to the projecti

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Springer Science+Business Media LLC 2010

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Riemannian Geometry of Contact and Symplectic Manifolds978-0-8176-4959-3Series ISSN 0743-1643 Series E-ISSN 2296-505X

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Progress in Mathematicshttp://image.papertrans.cn/r/image/830318.jpg