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Riemannian Geometry of Contact and Symplectic Manifolds
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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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Slant submanifolds of lorentzian sasakian and para sasakian manifolds
TL;DR: In this paper, the notion of slant submanifolds of a Lorentzian almost contact manifold and of a almost para contact mani- fold was introduced, and the concept of almost contact manifolds was defined.
Journal ArticleDOI
Ricci solitons on 3-dimensional cosymplectic manifolds
TL;DR: In this paper, it was shown that if a 3-dimensional cosymplectic manifold M3 admits a Ricci soliton, then either M3 is locally flat or the potential vector field is an infinitesimal contact transformation.
Journal ArticleDOI
Geometric structures associated with a contact metric $(\kappa,\mu)$-space
TL;DR: In this paper, it was shown that any contact metric admits a canonical paracontact metric structure which is compatible with the contact form, proving that it verifies a nullity condition.
Journal ArticleDOI
RICCI SOLITONS ON THREE-DIMENSIONAL $\eta$-EINSTEIN ALMOST KENMOTSU MANIFOLDS
Yaning Wang,Ximin Liu +1 more
TL;DR: In this article, it was shown that the Ricci soliton of a three-dimensional (3D)-Einstein almost-Einstein soliton is a Ricci manifold of constant sectional curvature.
Journal ArticleDOI
On almost cosymplectic (−1, μ, 0)-spaces
Piotr Dacko,Zbigniew Olszak +1 more
TL;DR: In this paper, a complete local description of almost cosymplectic (−1, μ, 0)-spaces is established: "models" of such spaces are constructed, and it is noted that a given almost cosyplectic (− 1, μ 0)-space is locally isomorphic to a corresponding model.