Some Geometry of Affine Immersion of General Co-dimension
Silas Longwap *
Department of Mathematics, Faculty of Natural Sciences, University of Jos, P. M. B 2084, Plateau State, Nigeria.
Homti E. Nahum
Department of Mathematics, Faculty of Natural Sciences, University of Jos, P. M. B 2084, Plateau State, Nigeria.
Gukat G. Bitrus
Department of Mathematics and Computer Science, Federal University of Kashere, P. M. B 0182, Gombe State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
After a careful study of some works of servaral authors on affine immersion of co-dimension one [1], co-dimension two [2], co-dimension three [3] and co-dimension four [4], we extend some of thier fundamental equations to affine immersion of genaral co-dimension p. Furthermore, we extend some theorem of Frank Dillen at el in [5] to affine immersion of general co-dimension and obtain the divisibility of the cubic forms by the second fundamental forms.
Keywords: Affine connections, affine immersion, general co-dimension.