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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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Totally geodesic submanifolds of a trans-Sasakian manifold
TL;DR: In this paper, the authors considered invariant submanifolds of a trans-Sasakian manifold and obtained the conditions under which the sub manifold is geodesic.
Maps between almost Kahler manifolds and framed '-manifolds
TL;DR: In this article, it was shown that any holomorphic map between an almost Kahler manifold and a metric framed manifold is a harmonic map with the minimum energy in its homotopy class.
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On anti-invariant semi-Riemannian submersions from Lorentzian (para)Sasakian manifolds
TL;DR: In this article, a semi-Riemannian submersion from Lorentzian almost contact manifolds is studied and necessary and sufficient conditions for the characteristic vector field to be vertical or horizontal.
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On Finsler Manifolds whose Tangent Bundle has the g-NATURAL Metric
Esmaeil Peyghan,Akbar Tayebi +1 more
TL;DR: In this paper, the authors introduced a Riemannian metric and a family of framed f-structures on the slit tangent bundle of a Finsler manifold and proved that the structure is Sasakian if and only if Fn is of positive constant curvature 1.
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Non-symmetric Riemannian gravity and Sasaki-Einstein 5-manifolds.
TL;DR: In this article, the existence of a connection with skew-symmetric torsion satisfying the Einstein metricity condition is shown to exist on an almost contact metric manifold exactly when it is D-homogeneous to a cosymplectic manifold.