In the present paper we classify all surfaces in 3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space 3 is the catenoid.
In this paper we obtain all invariant, anti-invariant and submanifolds in endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.
We introduce a torsion free linear connection on a hypersurface in a Sasakian manifold on which we have defined in natural way a -structure of -codimension 2. We study the curvature properties of this connection and we give some interesting examples.
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