We give a complete classification of surfaces with parallel second fundamental form in 3-dimensional Bianchi-Cartan-Vranceanu spaces.

Abstract. In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.2000 Mathematics Subject Classification: Primary 53B20, 53B25; Secondary 53B50, 53C25, 53C80.

We introduce the notion of D-homothetic bi-warping and starting from a Sasakian manifold M , we construct a family of Kählerian structures on the product R × M. After, we investigate conditions on the product of a cosymplectic or Kenmotsu manifold and the real line to be a family of conformal Kähler manifolds. We construct several examples.

PARALLEL SURFACES IN THE REAL SPECIAL LINEAR GROUP SL(2,R)MOHAMED BELKHELFA, FRANKI DlLLEN AND JUN-ICHI INOGUCHI Dedicated to Professor Koichi Ogiue on his sixtieth birthday We show that the only parallel surfaces in SL(2, M) are rotational surfaces with constant mean curvature.

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