Book•
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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25 Jan 2019
TL;DR: In this paper, the authors studied a Kenmotsu manifold admitting a quarter-symmetric metric connection whose conharmonic curvature tensor satisfies certain curvature conditions.
Abstract: The object of the present paper is to study a Kenmotsu manifold admitting a quarter-symmetric metric connection whose conharmonic curvature tensor satisfies certain curvature conditions.
6 citations
Cites background from "Riemannian Geometry of Contact and ..."
...For more details we refer to Blair’s books ([6],[7])....
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01 Jan 2013
TL;DR: In this article, the Chinea-Gonzales class of almost contact metric manifold locally realized as double-twisted product manifolds I ×(λ 1,λ 2)F, I being an open interval, F an almost Hermitian manifold and λ 1, λ 2smooth positive functions are studied.
Abstract: We determine the Chinea-Gonzales class of almost contact metricmanifolds locally realized as double-twisted product manifolds I ×(λ1,λ2)F ,I being an open interval, F an almost Hermitian manifold and λ1, λ2smoothpositive functions. Several subclasses are studied. We also give an explicitexpression for the cosymplectic defect of any manifold in the considered classand derive several consequences in dimensions 2n + 1 ≥ 5. Explicit formulasfor two algebraic curvature tensor fields are obtained. In particular cases, thisallows to state interesting curvature relations
6 citations
Posted Content•
TL;DR: In this paper, the authors construct families of complex structures on compact manifolds by means of normal almost contact structures (nacs) so that each complex manifold in the family has a non-singular holomorphic flow.
Abstract: We construct some families of complex structures on compact manifolds by means of normal almost contact structures (nacs) so that each complex manifold in the family has a non-singular holomorphic flow. These families include as particular cases the Hopf and Calabi-Eckmann manifolds and the complex structures on the product of two normal almost contact manifolds constructed by Morimoto. We prove that every compact Kaehler manifold admitting a non-vanishing holomorphic vector field belongs to one of these families and is a complexificacion of a normal almost contact manifold. Finally we show that if a complex manifold obtained by our constructions is Kaehlerian the Euler class of the nacs (a cohomological invariant associated to the structure) is zero. Under extra hypothesis we give necessary and sufficient conditions for the complex manifolds so obtained to be Kaehlerian.
6 citations
TL;DR: In this paper, the Integrability conditions of dis-tributions D and RadTM on radical transversal light-like submanifolds and screen slant RLS of indefinite para-Sasakian manifolds have been obtained.
Abstract: In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of dis- tributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, have been obtained. We also study totally contact umbilical radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds.
6 citations
Posted Content•
TL;DR: In this article, the Ricci curvature tensor of a manifold endowed with metric contact pairs for which the two characteristic foliations are orthogonal has been studied, and it has been shown that flat associated metrics can only exist if the leaves of the characteristic foliation are at most three-dimensional.
Abstract: We consider manifolds endowed with metric contact pairs for which the two characteristic foliations are orthogonal. We give some properties of the curvature tensor and in particular a formula for the Ricci curvature in the direction of the sum of the two Reeb vector fields. This shows that metrics associated to normal contact pairs cannot be flat. Therefore flat non-K\"ahler Vaisman manifolds do not exist. Furthermore we give a local classification of metric contact pair manifolds whose curvature vanishes on the vertical subbundle. As a corollary we have that flat associated metrics can only exist if the leaves of the characteristic foliations are at most three-dimensional.
6 citations