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Riemannian Geometry of Contact and Symplectic Manifolds
TLDR
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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Real hypersurfaces with a special transversal vector field
TL;DR: In this paper, real affine hypersurfaces of the complex space C are studied and properties of the structure determined by a J-tangent transversal vector field are proved.
Journal ArticleDOI
Sasakian structures on products of real line and Kahlerian manifold
TL;DR: In this paper, the authors constructed a Sasakian manifold by the product of real line and K\"{a}hlerian manifold with exact K-a-hler form.
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Geometric numerical integration of Li\'enard systems via a contact Hamiltonian approach
TL;DR: Focusing on the paradigmatic example of the van der Pol oscillator, it is demonstrated that these integrators are particularly stable and preserve the qualitative features of the dynamics, even for relatively large values of the time step and in the stiff regime.
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Critical point equation on a class of almost Kenmotsu manifolds
Dibakar Dey,Pradip Majhi +1 more
TL;DR: In this article, it was shown that if a non-constant solution of the critical point equation of a connected non-compact manifold admits a nonconstant function, then the manifold is locally isometric to the Ricci flat manifold and the function is harmonic.
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Einstein and $$\eta $$η-Einstein Sasakian submanifolds in spheres
TL;DR: In this paper, a complete classification of compact Sasakian immersions into the odd-dimensional sphere equipped with the standard Sasakians structure is presented. But the authors only consider the case where the codimension of the immersion is 4.