SOME PROPERTIES OF THE ATTACHED SURFACE TO THE GIVEN SURFACE V3 IN SPACE Ep+3

Abstract

Subject of research: Attached surface to the given surface V₃ in space E_p+3. Goal of research: Investigation of properties of attached surface to the given surface V₃ in space E_p+3. Research methods: Cartan’s method of external forms and moving reper method. Received results: The following properties of attached surface to the given surface V₃ in space E_p+3 are proved: а) The attached surface cannot be a second order cone; necessary conditions are found for the; b) Attached surface to be a hyperbola of index t; c) Attached surface to be an ellipsoid. Difference of research results: Since for the first time we consider the case, when : p=3, n=p+3, the obtained results are new. Recommendations for science and practice: The obtained results are recommended for further research in the theory of surfaces of differential geometry.