The purpose of this paper is to study the second fundamental form of some submanifolds M in Euclidean spaces E" which have flat normal connection. As such, Theorem gives precise expressions for the (essentially 2) Weingarten maps of all 4-dimensional Emstem submanifolds in E6, which are specialized in Corollary 2 to the Rcciflat submanifolds. The main part ofthis paper deals with fiat submanifo...

1. Algebraical, geometrical and analytical aspects of the theory of non-linear differential equations have been actively investigated recently. One of the problems appearing here is the problem of obtaining solutions of corresponding equations in explicit form, As known the general solution must be parametrized by the 2n arbitrary functions in the case o f n equations. Examples are well known: ...

frangibility and short life of textile in comparison to other cultural inheritances of iran led to disappearance of this precious object through the centuries. hence we must focus on other documents like written documents or visual representations to defining their essence. these records can demonstrate their materials quality, patterns, producing centers. the present research tries to investig...

Over the last 20 years, the voice of business and its impact upon Australian vocational education have transformed. These changes range from enterprise reluctance to be involved through to industry determining what is taught and assessed, and how, as well as the principles for administering vocational education, and attempts to use vocational education to reform the schooling system. These tran...