Corank one mono-germs , n < p, of -codimension one are classified by giving an explicit normal form.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-6, author = {Kevin Houston}, title = {On the classification of real mono-germs of corank one and codimension one}, journal = {Banach Center Publications}, volume = {65}, year = {2004}, pages = {77-84}, zbl = {1062.58036}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-6} }
Kevin Houston. On the classification of real mono-germs of corank one and codimension one. Banach Center Publications, Tome 65 (2004) pp. 77-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-6/