Sasakian manifolds with vanishing contact Bochner curvature tensor and constant scalar curvature
Scalar-flat Kähler metrics with SU (2) symmetry.
Scattering matrix in conformal geometry
Second order parallel tensors on generalized Sasakian space forms and semi parallel hypersurfaces in Sasakian space forms.
Second order parallel tensors on -contact metric manifolds.
Second order parallel tensors on – Sasakian manifold.
Sectional curvatures of minimal hypersurfaces immersed in
Seiberg Witten invariants and uniformizations.
Selection Rules for Topology Change
Self-dual Kähler manifolds and Einstein manifolds of dimension four
Selfdual spaces with complex structures, Einstein-Weyl geometry and geodesics
We study the Jones and Tod correspondence between selfdual conformal -manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl -manifolds, and prove that invariant complex structures correspond to shear-free geodesic congruences. Such congruences exist in abundance and so provide a tool for constructing interesting selfdual geometries with symmetry, unifying the theories of scalar-flat Kähler metrics and hypercomplex structures with symmetry. We also show that in the presence...
Semi-invariant submanifolds of a Lorentzian para-Sasakian manifold.
Semi-invariant submanifolds of a Sasakian space form
Semi-parallel CR submanifolds in a complex space form
We show that there is no proper CR submanifold with semi-flat normal connection and semi-parallel second fundamental form in a complex space form with non-zero constant holomorphic sectional curvature such that the dimension of the holomorphic tangent space is greater than 2.
Semiparallel isometric immersions of 3-dimensional semisymmetric Riemannian manifolds
A Riemannian manifold is said to be semisymmetric if . A submanifold of Euclidean space which satisfies is called semiparallel. It is known that semiparallel submanifolds are intrinsically semisymmetric. But can every semisymmetric manifold be immersed isometrically as a semiparallel submanifold? This problem has been solved up to now only for the dimension 2, when the answer is affirmative for the positive Gaussian curvature. Among semisymmetric manifolds a special role is played by the foliated...
Semi-symmetric four dimensional neutral Lie groups
The present paper is concerned with obtaining a classification regarding to four-dimensional semi-symmetric neutral Lie groups. Moreover, we discuss some geometric properties of these spaces. We exhibit a rich class of non-Einstein Ricci soliton examples.
Singer-Thorpe bases for special Einstein curvature tensors in dimension 4
Let be a 4-dimensional Einstein Riemannian manifold. At each point of , the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor at . In this basis, up to standard symmetries and antisymmetries, just components of the curvature tensor are nonzero. For the space of constant curvature, the group acts as a transformation group between ST bases at and for the so-called 2-stein curvature tensors, the group acts as a transformation group...
Singular Moment Maps and Quaternionic Geometry
Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry
We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant (particularly...
Slant and pseudo-slant submanifolds in -manifolds
We show new results on when a pseudo-slant submanifold is a LCS-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudo-slant product and give necessary and sufficient conditions for a pseudo-slant submanifold to be the pseudo-slant product. Also we give an example of a slant submanifold...