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Riemannian Geometry of Contact and Symplectic Manifolds
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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 Indexread more
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On Products of Generalized Geometries
Ralph R. Gomez,Janet Talvacchia +1 more
TL;DR: In this paper, the authors address what generalized geometric structures are possible on products of spaces that each admit generalized geometries and draw attention to the relationship of the Courant bracket to the classical notion of normality for almost contact structures.
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SLANT AND LEGENDRE CURVES IN BERGER $su(2)$: THE LANCRET INVARIANT AND QUANTUM SPHERICAL CURVES
TL;DR: In this article, the authors derived a Lancret-type invariant for the Legendre curves on the exponential map and showed that the curvature and torsion of these curves can be characterized using the scalar product between the normal at the curve and the vertical vector field.
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Ricci Curvature, Reeb Flows and Contact 3-Manifolds
TL;DR: In this paper, the Ricci curvature of a Reeb vector field for the contact structure of a contact 3-manifold has been studied and it has been shown that every admissible function can be realized as such curvature for a singular metric which is an honest compatible metric away from a measure zero set.
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Singular Contact Geometry and Beltrami Fields in Cholesteric Liquid Crystals
TL;DR: In this paper, the authors introduce the notion of singular contact structures, a generalisation of regular contact structures where the plane field may have singularities at isolated points, and characterize the class of singularities that may arise in such structures, as well as the subclass of singularity that can occur in a Beltrami field.
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Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator
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TL;DR: In this article, the Ricci operator of a trans-Sakian manifold is invariant along Reeb flow if and only if the manifold is an α -Sasakian, cosymplectic manifold or a space of constant sectional curvature.