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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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Pseudo-symmetric contact 3-manifolds III
TL;DR: In this paper, the authors show that all Sasakian 3-manifolds are pseudo-symmetric spaces of constant type, and that they are homogeneous 3-menifolds.
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Canonical-type connection on almost contact manifolds with B-metric
Mancho Manev,Miroslava Ivanova +1 more
TL;DR: The canonical-type connection on the almost contact manifolds with B-metric is constructed in this paper, and it is proved that its torsion is invariant with respect to a subgroup of the general conformal transformations.
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On cohomology of almost complex 4-manifolds
TL;DR: In this paper, the authors further investigated properties of the dimension of a closed almost Hermitian 4-manifold using metric compatible almost complex structures and proved that the dimension h_J^-=0.
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Symmetries of null Geometry in Indefinite Kenmotsu Manifolds
TL;DR: In this article, it was shown that locally symmetric and semi-symmetric null hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field, are totally geodesic and parallel.
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Bochner and conformal flatness on normal complex contact metric manifolds
TL;DR: In this paper, it was shown that normal complex contact metric manifolds that are Bochner flat must have constant holomorphic sectional curvature 4 and be Kahler-flat.