Generalized cotangency sets in projective spaces

The notion of cotangency set in the projective plane over any field was int roduced by Bruen and Fisher [1]. They proved that a cotangency set never co ntains a quadrangle and deduced several theorems from this fact. In this pa per a generalized definition of cotangency sets in the n-dimensional projec tive space is given. We prove some theorems about quadrics and Hermitian va rieties which are consequences of the properties of cotangency sets.