On quasi-Sasakian 3-manifolds admitting η-Ricci solitons

Characterization of three-dimensional Riemannian manifolds with a type of semi-symmetric metric connection admitting Yamabe soliton

Abstract: We characterize the three-dimensional Riemannian manifolds equipped with a semi-symmetric metric ρ -connection under the assumption that the Riemannian metric is a Yamabe soliton. It is shown that a three-dimensional Riemannian manifold endowed with a semi-symmetric ρ -connection, whose metric is Yamabe soliton, is a manifold of constant sectional curvature − 1 and the Yamabe soliton is expanding with soliton constant − 6 . Finally, we give an example of a three-dimensional Riemannian manifold and validate our findings.

Characterization of perfect fluid spacetimes admitting gradient η-Ricci and gradient Einstein solitons

Abstract: We set the goal to study the properties of perfect fluid spacetimes endowed with the gradient η -Ricci and gradient Einstein solitons.

Curvature Properties of η-Ricci Solitons on Para-Kenmotsu Manifolds

Abstract: In the present paper, we study curvature properties of η-Ricci solitons on para-Kenmotsu manifolds. We obtain some results of η-Ricci solitons on para-Kenmotsu manifolds satisfying R(ξ,X).C = 0, R(ξ,X).M̃ = 0, R(ξ,X).P = 0, R(ξ,X).C̃ = 0 and R(ξ,X).H = 0, where C, M̃ , P , C̃ and H are a quasi-conformal curvature tensor, a M -projective curvature tensor, a pseudo-projective curvature tensor, and a concircular curvature tensor and conharmonic curvature tensor, respectively.

Gradient Yamabe and Gradient m-Quasi Einstein Metrics on Three-dimensional Cosymplectic Manifolds

Abstract: In this paper, we characterize the gradient Yamabe and the gradient m-quasi Einstein solitons within the framework of three-dimensional cosymplectic manifolds.

Riemannian Geometry of Contact and Symplectic Manifolds

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

Contact manifolds in Riemannian geometry

Abstract: Contact manifolds.- Almost contact manifolds.- Geometric interpretation of the contact condition.- K-contact and sasakian structures.- Sasakian space forms.- Non-existence of flat contact metric structures.- The tangent sphere bundle.

Branes at conical singularities and holography

Abstract: For supergavrity solutions which are the product of an anti-de Sitter space with an Einstein space X, we study the relation between the amount of supersymmetry preserved and the geometry of X. Depending on the dimension and the amount of supersymmetry, the following geometries for X are possible, in addition to the maximally supersymmetric spherical geometry: Einstein-Sasaki in dimension 2k+1, 3-Sasaki in dimension 4k+3, 7-dimensional manifolds of weak G_2 holonomy and 6-dimensional nearly Kaehler manifolds. Many new examples of such manifolds are presented which are not homogeneous and have escaped earlier classification efforts. String or M theory in these vacua are conjectured to be dual to superconformal field theories. The brane solutions interpolating between these anti-de Sitter near-horizon geometries and the product of Minkowski space with a cone over X lead to an interpretation of the dual superconformal field theory as the world-volume theory for branes at a conical singularity (cone branes). We propose a description of those field theories whose associated cones are obtained by (hyper-)Kaehler quotients.