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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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The geometry of 3-quasi-sasakian manifolds
TL;DR: In this article, it was shown that 3-Sasakian manifolds are multiply foliated by four distinct fundamental foliations, which can be used to link the 3-Siamese manifolds to the more famous hyper-Kahler and quaternionic kahler geometries.
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Para-Sasaki-like Riemannian manifolds and new Einstein metrics
TL;DR: In this paper, a new class of paracontact paracomplex Riemannian manifold arising from certain cone construction is introduced, called para-Sasaki-like manifold and given explicit examples.
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Harmonicity and minimality of distributions on Riemannian manifolds via the intrinsic torsion.
TL;DR: In this paper, the authors consider a q-dimensional distribution as a section of the Grassmannian bundle Gq(M ) of q-planes and derive, in terms of the intrinsic torsion of the corresponding S(O(q)×O(n−q))-structure, the conditions that this map must satisfy in order to satisfy the conditions critical for the functionals energy and volume.
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Variations of the total mixed scalar curvature of a distribution
TL;DR: In this article, the authors examined the total mixed scalar curvature of a smooth manifold endowed with a distribution as a functional of a pseudo-Riemannian metric and developed variational formulas for quantities of extrinsic geometry of the distribution and used this key and technical result to find the critical points of this action.
Posted Content
On basic curvature identities for almost (para)contact metric manifolds
TL;DR: In this article, the curvature identity for contact and paracontact metric manifold is proved for a wider class of manifolds, which generalizes results presented in above mentioned publications, and some properties of almost (para)hermitian structure on a special semiproduct of R+ and an almost contact metric manifold.