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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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Sub-Riemannian Curvature in Contact Geometry
TL;DR: In this article, the authors compare different notions of curvature on contact sub-Riemannian manifolds and show that all these curvatures are encoded in the asymptotic expansion of the horizontal derivatives of the sub-riemannians distance.
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Explicit formulas for biharmonic submanifolds in sasakian space forms
Dorel Fetcu,Cezar Oniciuc +1 more
TL;DR: In this article, the authors classify all biharmonic Legendre curves in a Sasakian space form and obtain their explicit parametric equations in the (2n + 1)-dimensional unit sphere endowed with the canonical and deformed structures defined by Tanno.
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Improved Chen–Ricci inequality for curvature-like tensors and its applications
TL;DR: In this paper, Chen-Ricci inequality and improved Chen Ricci inequality for curvature-like tensors were presented and applied to Lagrangian and Kaehlerian slant submanifolds of complex space forms.
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Bishop and Laplacian Comparison Theorems on Three-Dimensional Contact Sub-Riemannian Manifolds with Symmetry
TL;DR: In this paper, the authors prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three-dimensional contact sub-Riemannian manifolds with symmetry, and prove a similar theorem for 3-D contact subriemannians with symmetry.
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Indefinite Almost Paracontact Metric Manifolds
TL;DR: In this paper, the authors introduced the concept of almost paracontact manifold, and in particular, of ''para-Sasakian'' manifolds, and showed that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it cannot admit an''para'' Sasakian structure.