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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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Journal ArticleDOI
Generalized Contact Structures
Yat Sun Poon,Aïssa Wade +1 more
TL;DR: In this article, the integrability of generalized almost contact structures was studied and conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids.
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A note on Almost Riemann Soliton and gradient almost Riemann soliton.
Krishnendu De,Uday Chand De +1 more
TL;DR: In this paper, it was shown that if the metric of a non-cosymplectic normal almost contact metric manifold is Riemann soliton with divergence-free potential vector field (Z), then the manifold is quasi-Sakian and is of constant sectional curvature -$\lambda.
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The geometry of 3-quasi-Sasakian manifolds
TL;DR: In this article, it was shown that 3-Sasakian manifolds of rank 4l+1 are 3-cosymplectic and 3-alpha-Sakian.
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Slant Curves and Contact Magnetic Curves in Sasakian Lorentzian 3-Manifolds
TL;DR: Using a Lorentzian cross product, it is proved that the ratio of κ and τ − 1 is constant along a Frenet slant curve in a Sasakian LorentZian three-manifold.
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On ∅-recurrent contact metric manifolds
TL;DR: In this paper, it was shown that a 3-dimensional manifold M is a recurrent N(k)-contact metric manifold if and only if it is flat, which implies that there exists no locally ε-symmetric manifold which is not symmetric.