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Riemannian Geometry of Contact and Symplectic Manifolds

08 Jan 2002-
TL;DR: 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 Index

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Journal ArticleDOI
TL;DR: In this article, the spectral and ergodic properties of Schrodinger operators on a compact connected Riemannian manifold M without boundary were studied, and it was shown that if M carries an isometric and effective action of the compact connected Lie group G, then it is possible to obtain a generalized equivariant version of the semiclassical Weyl law with an estimate for the remainder.

6 citations

Journal Article
TL;DR: In this paper, the E-Bochner curvature tensor B e satisfying R:B e = 0, B e :R = 0 and S:S = 0 in an ndimensional N(k)-contact metric manifold was studied.
Abstract: The object of the present paper is to study E-Bochner curvature tensor B e satisfying R:B e = 0, B e :R = 0, B e :B e = 0 and B e :S = 0 in an ndimensional N(k)-contact metric manifold.

6 citations

Journal ArticleDOI
01 Jun 2010
TL;DR: In this paper, the authors studied homogeneous Kahler structures on a non-compact Hermitian symmetric space and their lifts to homogeneous Sasakian structures on the total space of a principal line bundle over it.
Abstract: We study homogeneous Kahler structures on a non-compact Hermitian symmetric space and their lifts to homogeneous Sasakian structures on the total space of a principal line bundle over it, and we analyse the case of the complex hyperbolic space.

6 citations


Cites background from "Riemannian Geometry of Contact and ..."

  • ...Sasakian manifolds can also be characterized as normal contact metric manifolds and they are in some sense odd-dimensional analogues of Kähler manifolds [3,4]....

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Journal ArticleDOI
TL;DR: In this article, the authors studied a class of almost contact Riemannian manifolds called generalized Kenmotsu manifolds and showed that the curvature of these manifolds is a locally warped product space.
Abstract: In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds which later are called a Kenmotsu manifold. In this paper, we study Kenmotsu manifolds with \((2n+s)\)-dimensional $s$-contact metric manifold that we call generalized Kenmotsu manifolds.\ Necessary and sufficient condition is given for a \(s\)-contact metric manifold to be a generalized Kenmotsu manifold. We show that a generalized Kenmotsu manifold is a locally warped product space. In addition, we study some curvature properties of generalized Kenmotsu manifolds. Moreover, we obtain that the \(\varphi\)-sectional curvature of any semi-symmetric and projective semi-symmetric \((2n+s)\)-dimensional generalized Kenmotsu manifold is \(-s\).

6 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied conharmonically symmetric, ǫ-conharmony-flat, and à −conharmonicity-flat contact metric manifolds.
Abstract: The object of the present paper is to characterize 𝑁(𝑘)-contact metric manifolds satisfying certain curvature conditions on the conharmonic curvature tensor. In this paper we study conharmonically symmetric, 𝜉-conharmonically flat, and 𝜙-conharmonically flat 𝑁(𝑘)-contact metric manifolds.

6 citations