In this paper, we mainly study local structures and curvatures of the almost α-para-Kenmotsu manifolds. particular, locally symmetric manifolds satisfying certain nullity conditions are classified.

A submanifold is called tangentially degenerate if its Gauss mapping is degenerate. The investigation of tangentially degeneracy of submanifolds has long history. For example the classification of surfaces in R with degenerate Gauss mapping is equivalent to the classification of flat surfaces in R. As a result, that is one of planes, cylinders, cones or tangent developable surfaces. In this pap...

Using the Dehn presentation of a link group, a short elementary proof is given of the result: The number of components of a link arising from a medial graph M( ) by resolving vertices is equal to the nullity of the mod-2 Laplacian matrix of .