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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
Citations
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Journal ArticleDOI
The curvature tensor of (\kappa ,\mu ,\nu )-contact metric manifolds
TL;DR: In this article, the Riemann curvature tensor of contact metric manifolds has been studied in dimension 3 and the necessary and sufficient conditions for them to be conformally flat.
Journal ArticleDOI
Integrable (3+1)-dimensional system with an algebraic Lax pair
TL;DR: It is shown that the class of integrable ( 3 + 1 ) -dimensional dispersionless systems with nonisospectral Lax pairs is significantly more diverse than it appeared before.
Journal ArticleDOI
H-contact unit tangent sphere bundles of Riemannian manifolds
TL;DR: In this paper, it was shown that the unit tangent bundle of a Riemannian manifold M equipped with the standard contact metric structure is H-contact if and only if M is 2-stein.
Journal ArticleDOI
Non-existence of real hypersurfaces equipped with recurrent structure Jacobi operator in nonflat complex planes
Th. Theofanidis,Ph. J. Xenos +1 more
TL;DR: In this paper, the authors proved the nonexistence of real hypersurfaces with recurrent structure Jacobi operators in non-flat complex planes, where the Jacobi operator is defined in terms of the number of vertices.
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On non-gradient $(m,\rho)$-quasi-Einstein contact metric manifolds.
TL;DR: In this article, the Ricci solitons and their analogs within the framework of contact geometry were studied and proved to be locally isometric to the product of a Euclidean space and a sphere of constant curvature.