Book•
Riemannian Geometry of Contact and Symplectic Manifolds
08 Jan 2002-
TL;DR: In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.
Abstract: Preface * 1. Symplectic Manifolds * 2. Principal S1-bundles * 3. Contact Manifolds * 4. Associated Metrics * 5. Integral Submanifolds and Contact Transformations * 6. Sasakian and Cosymplectic Manifolds * 7. Curvature of Contact Metric Manifolds * 8. Submanifolds of Kahler and Sasakian Manifolds * 9. Tangent Bundles and Tangent Sphere Bundles * 10. Curvature Functionals and Spaces of Associated Metrics * 11. Negative Xi-sectional Curvature * 12. Complex Contact Manifolds * 13. Additional Topics in Complex Geometry * 14. 3-Sasakian Manifolds * Bibliography * Subject Index * Author Index
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TL;DR: In this paper, the authors obtained the parametric equations of all biharmonic Legendre curves and Hopf cylinders in the 3D unit sphere endowed with the modified Sasakian structure defined by Tanno.
Abstract: We obtain the parametric equations of all biharmonic Legendre curves and Hopf cylinders in the 3-dimensional unit sphere endowed with the modified Sasakian structure defined byTanno.
20 citations
Cites background from "Riemannian Geometry of Contact and ..."
...Endowed with these tensors, S 3 becomes a Sasakian space form with ϕ 0 -sectional curvature 1 (see [4])....
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TL;DR: In this paper, a twisted supersymmetric Yang-Mills theory on the five-dimensional sphere using localisation techniques is presented, and the twistor construction of this equation when formulated on K-contact manifolds and the discussion of its integrability properties is discussed.
Abstract: Recently, Kallen & Zabzine computed the partition function of a twisted supersymmetric Yang-Mills theory on the five-dimensional sphere using localisation techniques. Key to their construction is a five-dimensional generalisation of the instanton equation to which they refer as the contact instanton equation. Subject of this article is the twistor construction of this equation when formulated on K-contact manifolds and the discussion of its integrability properties. We also present certain extensions to higher dimensions and supersymmetric generalisations.
20 citations
TL;DR: In this paper, the authors employ a recently devised metric within the Geometrothermodynamics program to study ordinary thermodynamic systems and present a thorough analysis for the ideal gas, the van der Waals fluid, the one dimensional Ising model and some other systems of cosmological interest.
20 citations
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TL;DR: In this paper, a Riemanian metric on the tangent bundle of a Riemannian manifold was proposed, which generalizes the Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to a structure of locally conformal almost K\"ahlerian manifold.
Abstract: In this paper we study a Riemanian metric on the tangent bundle $T(M)$ of a Riemannian manifold $M$ which generalizes the Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to $T(M)$ a structure of locally conformal almost K\"ahlerian manifold We found conditions under which $T(M)$ is almost K\"ahlerian, locally conformal K\"ahlerian or K\"ahlerian or when $T(M)$ has constant sectional curvature or constant scalar curvature
20 citations
TL;DR: In this paper, the harmonicity of (φ,φ′)-holomorphic maps between almost contact metric manifolds, in particular horizontally conformal holomorphic submersions, was studied.
Abstract: We study (φ,φ′)-holomorphic maps between almost contact metric manifolds, in particular horizontally conformal (φ,φ′)-holomorphic submersions, and obtain some criteria for the harmonicity of such maps.
20 citations