Themis Koufogiorgos

CONTACT METRIC MANIFOLDS SATISFYING A NULLITY CONDITION

This paper presents a study of contact metric manifolds for which the characteristic vector field of the contact structure satisfies a nullity type condition, condition (*) below. There are a number of reasons for studying this condition and results concerning it given in the paper: There exist examples in all dimensions; the condition is invariant underD-homothetic deformations; in dimensions>5 the condition determines the curvature completely; and in dimension 3 a complete, classification is given, in particular these include the 3-dimensional unimodular Lie groups with a left invariant metric.

On the Existence of a New Class of Contact Metric Manifolds

A new class of 3-dimensional contact metric manifolds is found. Moreover it is proved that there are no such manifolds in dimensions greater than 3.

Conformally flat contact metric manifolds

Abstract. A couple of classes of conformally flat contact metric manifolds have been classified. Conformally flat contact manifolds have been characterized as hypersurfaces of 4-dimensional Kaehler Einstein (in particular, Calabi-Yau) manifolds.

Contact metric manifolds

In this paper we study contact metric manifoldsM2n+1(ϕ, η, ξ,g) with characteristic vector field ξ belonging to thek-nullity distribution. Moreover we prove that there exist i) nonK-contact, contact metric manifolds of dimension greater than 3 with Ricci operator commuting with ϕ and ii) 3-dimensional contact metric manifolds with non-zero constant ϕ-sectional curvature.

On a Class of Contact Riemannian 3-Manifolds

In this paper we classify 3-dimensional complete contact Riemannian manifolds satisfying the following condition “the characteristic vector field is an eigenvector of the Ricci operator with constant eigenvalue”. Moreover we prove that this condition is equivalent with some other characteristic ones.

Integral submanifolds of sasakian space forms % MathType!MTEF!2!1!+-% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXanrfitLxBI9gBaerbd9wDYLwzYbItLDharqqt% ubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq% -Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0x% fr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuam% aaBaaaleaacaaIXaGaaGimaaqabaGccqGH9aqpciGGSbGaaiOBaiaa% ysW7caWGRbWaaSbaaSqaaiaadsfacaaIXaaabeaakiaac+cacaWGRb% WaaSbaaSqaaiaadsfacaaIYaaabeaakiabg2da9iabgkHiTmaabmaa% baGaamyramaaBaaaleaacaWGHbaabeaakiaac+cacaWGsbaacaGLOa% GaayzkaaGaey41aq7aaiWaaeaadaqadaqaaiaadsfadaWgaaWcbaGa% aGOmaaqabaGccqGHsislcaWGubWaaSbaaSqaaiaaigdaaeqaaaGcca% GLOaGaayzkaaGaai4laiaacIcacaWGubWaaSbaaSqaaiaaikdaaeqa% aOGaaGjbVlaadsfadaWgaaWcbaGaamysaaqabaGccaGGPaaacaGL7b% GaayzFaaaaaa!5C4A!

This paper gives a classification of 3-dimensional integral submanifolds of 7-dimensional Sasakian space forms for which the covariant derivative of the second fundamental form is parallel to the characteristic vector field. In the case of the 7-sphere, when the submanifold is flat, the position vector is given explicitly. In the case of negative ϕ-sectional curvature an interesting example is given in detail.