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Abstract. We study the quaternion CR-submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR-submanifold.2000 Mathematics Subject Classification. 53C20, 53C21, 53C25.

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ABSTRACT. The purpose of the present study is to characterise the Grassmann manifold G (R) and its non compact dual G* (R) by means of a particular parallel tensor p,2 p,2 field T of type (1,3) and the Weingarten map on geodesic spheres.

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In this paper the surfaces of revolution without parabolic points, in the 3-dimensional LorentzMinkowski space are classified under the condition II r = A r where II is the Laplace operator with respect to the second fundamental form and A is a real 3 × 3 matrix. More precisely we prove that such surfaces are either minimal or Lorentz hyperbolic cylinders or pseudospheres of real or imaginary radius. (2000): 53A05, 53A07, 53C40. Mathematics Subject Classification