We study complex affine surfaces in ℂ⁴ with the transversal bundle defined by Nomizu and Vrancken. We classify the surfaces that have recurrent shape operators and parallel transversal metric.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-3-6, author = {Pawe\l\ Witowicz}, title = {Complex surfaces in C4 with recurrent shape operators}, journal = {Annales Polonici Mathematici}, volume = {92}, year = {2007}, pages = {265-276}, zbl = {1118.53010}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-3-6} }
Paweł Witowicz. Complex surfaces in ℂ⁴ with recurrent shape operators. Annales Polonici Mathematici, Tome 92 (2007) pp. 265-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-3-6/